# -*- coding: utf-8 -*-
# =============================================================================
# VERIF_EISENSTEIN.py
# Author: David Niedbala Giraudin (ORCID 0009-0009-1526-1178)
# Technical assistance: Claude (Anthropic)
# Ancillary file to: "Hecke eigenvalues in level 1 modulo powers of 2 and 3:
# Hatada's question (1981) and the Coleman-Stein conjecture",
# Sections 6 and 7 (Theorems N, O, P, R, S) and Section "Verification".
# These certificates provide the input data of Theorem O (Eisenstein law
# modulo 81 in every weight): a_7 == s_7 modulo 81 for every k; the other input,
# a_2**2 == s_2**2 modulo 81, is Theorem K, checked by VERIF_A2.py.
# -----------------------------------------------------------------------------
# Statements checked. For every eigenform f of level 1 and weight k, with
# s_l = 1 + l**(k-1):
#   (N)  l = 7, 13: a_l == s_l (mod 81) if k != 4 (mod 6), (mod 27) if k == 4 (mod 6);
#        l = 7, k == 4 (mod 6): T_7 - s_7 - 18 T_2 == 0 (mod 81) on L_k, hence a_7 == s_7 (mod 81);
#        l = 19   : a_l == s_l (mod 243) if k != 4 (mod 6), (mod 81) if k == 4 (mod 6);
#        l = 19, k == 4 (mod 6): T_19 - s_19 - 54 T_2 == 0 (mod 243) on L_k, hence
#                    a_19 == s_19 (mod 243) for every k (since 9 | a_2);
#        l = 5, 11: a_l**2 == s_l**2 (mod 81) if k != 4 (mod 6), a_l == 0 (mod 9) otherwise;
#        l = 17   : a_l**2 == s_l**2 (mod 243) if k != 4 (mod 6).
#   (O)  for k <= KMAX_O: a_n == sigma_{k-1}(n) (mod 81) for every n == 1 (mod 3)
#        (by Sturm's theorem on Gamma_0(9), n <= k suffices).
#   (P)  l == 1 (mod 3): a_l == s_l + u(l) (a_2**2 - s_2**2) (mod 243), u(l) = 0 if
#        l == 1 (mod 9), 1 otherwise; l == 2 (mod 3): a_l**2 == s_l**2 + u(l**2) (a_2**2 - s_2**2).
#   (R)  l == 1 (mod 9) and 3 a cube modulo l: a_l == s_l (mod 729);
#        l == -1 (mod 9): a_l**2 == s_l**2 (mod 729).
#   (S)  l, l' == 2 (mod 3): a_l a_l' == s_l s_l' + ut(l) ut(l') (a_2**2 - s_2**2) (mod 243),
#        ut(l) = -1, 1, 0 according as l == 2, 5, 8 (mod 9).
#
# RUN WITH PLAIN PYTHON 3. No library. No input needed.
# Running time: about two minutes. Memory: a few tens of MB. Progressive output.
#
# Part A: the 19 certificates (Lemma 8 generalized): for each certificate,
#         zeta (a combination of terms of the ideal I) is rebuilt, and the remainder
#         j = Xi - zeta is submitted to the vanishing criterion of Lemma 7 modulo 3**n,
#         for the indicated class w == r (mod 3). A witness shows that the target
#         alone does not satisfy the criterion.
# Part B: direct check of part A by action on forms of degree w.
# Part C: statement (O) for 12 <= k <= KMAX_O, at the level of eigenvalues:
#         characteristic polynomial of T_n on Hatada's lattice L_k, and
#         Newton polygon of P(x + sigma) (all slopes >= 4).
# Part D: statements (P), (R), (S) for 12 <= k <= KMAX_D on L_k, at the level of
#         eigenvalues (Newton polygon of the characteristic polynomial of the combined
#         operator), with witnesses showing that the correction term is necessary.
# =============================================================================
import sys
import time
from fractions import Fraction
from math import comb, gcd

KMAX_O = int(44)         # Part C: weights up to KMAX_O (running time grows quickly with k)
W_B_MAX = int(30)        # Part B: degrees w <= W_B_MAX
BUDGET = float(480.0)    # seconds: clean stop beyond this
PARTIE_B = True
PARTIE_C = True
KMAX_D = int(40)         # Part D: weights up to KMAX_D
PARTIE_D = True

T0 = time.time()

def dire(*a):
    print(*a, flush=True)

def v3(n):
    n = abs(int(n))
    if n == 0:
        return 10 ** 9
    v = 0
    while n % 3 == 0:
        n //= 3
        v += 1
    return v

# =============================================================================
# Tools: monoid of matrices modulo 3**n, representatives, Taylor expansion
# =============================================================================
def mulmod(g, h, N):
    a, b, c, d = g
    e, f, p, q = h
    return ((a * e + b * p) % N, (a * f + b * q) % N, (c * e + d * p) % N, (c * f + d * q) % N)

def elt(g, N, c=1):
    return {tuple(int(t) % N for t in g): int(c) % N}

def somme(N, *termes):
    out = {}
    for c, X in termes:
        for g, x in X.items():
            out[g] = (out.get(g, 0) + c * x) % N
    return {g: x for g, x in out.items() if x}

def produit(X, Y, N):
    out = {}
    for g, x in X.items():
        for h, y in Y.items():
            k = mulmod(g, h, N)
            out[k] = (out.get(k, 0) + x * y) % N
    return {g: x for g, x in out.items() if x}

REPS24 = []
_vus = set()
for _a in range(3):
    for _b in range(3):
        for _c in range(3):
            for _d in range(3):
                if (_a * _d - _b * _c) % 3 == 0:
                    continue
                _t = (_a, _b, _c, _d)
                _n = tuple((-x) % 3 for x in _t)
                if _t in _vus or _n in _vus:
                    continue
                _vus.add(_t)
                REPS24.append(_t)
CLASSE = {}
for _i, _r in enumerate(REPS24):
    CLASSE[_r] = _i
    CLASSE[tuple((-x) % 3 for x in _r)] = _i

def manin(n):
    out = []
    for a in range(1, n + 1):
        for d in range(1, n + 1):
            if a * d < n:
                continue
            for c in range(0, a):
                for b in range(0, d):
                    if a * d - b * c == n:
                        out.append((a, b, c, d))
    return out

KAPPA = [(4, 0, 0, 1), (1, 3, 0, 1), (1, 0, 3, 1), (1, 0, 0, 4)]

class Anneau:
    """the monoid modulo N = 3**n, its generators of I and the factors kappa_i - 1"""
    def __init__(self, n):
        self.n = n
        self.N = N = 3 ** n
        self.un = elt((1, 0, 0, 1), N)
        U = (1, N - 1, 1, 0)
        self.gens = {'S': somme(N, (1, self.un), (1, elt((0, -1, 1, 0), N))),
                     'U': somme(N, (1, self.un), (1, elt(U, N)), (1, elt(mulmod(U, U, N), N))),
                     'E': somme(N, (1, self.un), (1, elt((-1, 0, 0, 1), N)))}
        self.bfac = [somme(N, (1, elt(k, N)), (-1, self.un)) for k in KAPPA]
        self.repinv = []
        for r in REPS24:
            a, b, c, d = r
            di = pow((a * d - b * c) % N, -1, N)
            self.repinv.append(((d * di) % N, (-b * di) % N, (-c * di) % N, (a * di) % N))

    def terme(self, tok):
        code = tok[0]
        h = ord(tok[1]) - ord('a')
        al = [int(tok[2 + t]) for t in range(4)]
        c = int(tok[6:9])
        X = elt(REPS24[h], self.N)
        for t in range(4):
            for _ in range(al[t]):
                X = produit(X, self.bfac[t], self.N)
        return produit(self.gens[code], X, self.N), c

    def zeta(self, texte):
        acc = {}
        toks = ''.join(texte).split()
        for tok in toks:
            X, c = self.terme(tok)
            for g, x in X.items():
                acc[g] = (acc.get(g, 0) + c * x) % self.N
        return {g: x for g, x in acc.items() if x}, len(toks)

    def coord_kappa(self, k):
        """sigma_k (x**i y**j) = (p x + r y)**i (q x + s y)**j, k = (p, q; r, s) == I (mod 3) ;
        modulo 3**n: sum over delta of [ sum c(delta, A, B) C(i, A) C(j, B) ] x**(i+delta) y**(j-delta)"""
        p, q, r, s = k
        n, N = self.n, self.N
        out = {}
        for a in range(n):
            for b in range(n - a):
                for m in range(n - a - b):
                    for m2 in range(n - a - b - m):
                        val = (r ** a) * (q ** b) * ((p - 1) ** m) * ((s - 1) ** m2) * comb(a + m, a) * comb(b + m2, b)
                        cle = (b - a, a + m, b + m2)
                        out[cle] = (out.get(cle, 0) + val) % N
        return out

    def decompose(self, g):
        i = CLASSE[tuple(t % 3 for t in g)]
        k = mulmod(self.repinv[i], g, self.N)
        if k[0] % 3 != 1:
            k = tuple((-t) % self.N for t in k)
        if not ((k[0] - 1) % 3 == 0 and k[1] % 3 == 0 and k[2] % 3 == 0 and (k[3] - 1) % 3 == 0):
            raise ValueError('decomposition impossible')
        return i, k

    def critere_nul(self, X, r):
        """Lemma 7: true if the Mahler coefficients (in i and t, j = 3t + r - i, total degree < n)
        of all the polynomials f(h, delta) vanish modulo 3**n; then X acts by 0 modulo 3**n
        on the forms of even degree w, w == r (mod 3)."""
        n, N = self.n, self.N
        blocs = {}
        for g, x in X.items():
            h, k = self.decompose(g)
            for (dl, A, B), v in self.coord_kappa(k).items():
                bl = blocs.setdefault((h, dl), {})
                bl[(A, B)] = (bl.get((A, B), 0) + x * v) % N
        for bl in blocs.values():
            vals = [[sum(c * comb(i, A) * binom_entier(3 * t + r - i, B) for (A, B), c in bl.items())
                     for t in range(n)] for i in range(n)]
            for A in range(n):
                for B in range(n - A):
                    tot = 0
                    for u in range(A + 1):
                        for v in range(B + 1):
                            tot += (-1) ** (A - u + B - v) * comb(A, u) * comb(B, v) * vals[u][v]
                    if tot % N:
                        return False, len(blocs)
        return True, len(blocs)

def binom_entier(z, k):
    num = 1
    for t in range(k):
        num *= (z - t)
    f = 1
    for t in range(2, k + 1):
        f *= t
    return num // f

def image_monome(w, j, a, b, c, d, N=None):
    """coefficients of F(ax + cy, bx + dy) for F = x**j y**(w-j)"""
    A = [comb(j, s) * (a ** s) * (c ** (j - s)) for s in range(j + 1)]
    B = [comb(w - j, t) * (b ** t) * (d ** (w - j - t)) for t in range(w - j + 1)]
    out = [0] * (w + 1)
    for s, x in enumerate(A):
        if x:
            for t, y in enumerate(B):
                if y:
                    out[s + t] += x * y
    if N is not None:
        out = [x % N for x in out]
    return out

def cible(R, l, mode, a=None, b=None):
    """Xi in the ring modulo N: lin: T_l - (1 + l Lam_l) ; sq: T_l**2 - (1 + l Lam_l)**2 ;
    quad: T_l**2 + a(Lam_l) T_l + b(Lam_l), Lam_l = l.I acting by l**w"""
    N = R.N
    T = somme(N, *[(1, elt(g, N)) for g in manin(l)])
    Lam = elt((l, 0, 0, l), N)
    if mode == 'lin':
        return somme(N, (1, T), (-1, R.un), (-l, Lam))
    if mode == 'lin7k4':
        T2 = somme(N, *[(1, elt(g, N)) for g in manin(2)])
        return somme(N, (1, T), (-1, R.un), (-l, Lam), (-18, T2))
    if mode == 'lin19k4':
        T2 = somme(N, *[(1, elt(g, N)) for g in manin(2)])
        return somme(N, (1, T), (-1, R.un), (-l, Lam), (-54, T2))
    if mode == 'sq':
        sg = somme(N, (1, R.un), (l, Lam))
        return somme(N, (1, produit(T, T, N)), (-1, produit(sg, sg, N)))
    acc = produit(T, T, N)
    Lp = R.un
    for i in range(len(a)):
        acc = somme(N, (1, acc), (a[i], produit(Lp, T, N)), (b[i], Lp))
        Lp = produit(Lp, Lam, N)
    return acc

CERT_L19_R2M = (
    "Sa0001027 Sa0010027 Sb0000189 Sb0001054 Sb0100027 Sd0000030 Sd0001033 "
    "Sd0002016 Sd0003001 Sd0010033 Sd0011024 Sd0012001 Sd0020015 Sd0021002 "
    "Sd0030001 Sd0100006 Sd0101003 Sd0102002 Sd0110007 Sd0111002 Sd0200015 "
    "Sd0201001 Sd1000024 Sd1001001 Sd1020001 Sd1200002 Sd2000001 Se0000006 "
    "Se0001007 Se0002025 Se0003001 Se0010052 Se0012001 Se0020016 Se0021001 "
    "Se0030001 Se0100019 Se0101006 Se0102002 Se0110006 Se0111001 Se0120001 "
    "Se0200001 Se0300001 Se1000026 Se1001001 Se1010007 Se1100001 Se1200001 "
    "Se2000001 Sf0000165 Sf0001043 Sf0002025 Sf0003002 Sf0010065 Sf0011012 "
    "Sf0012001 Sf0020011 Sf0021001 Sf0030001 Sf0100023 Sf0101013 Sf0102002 "
    "Sf0110005 Sf0200018 Sf0210002 Sf0300002 Sf1000014 Sf1001001 Sf1010008 "
    "Sf1020001 Sf1100007 Sf2000001 Si0000003 Si0001056 Si0002005 Si0003002 "
    "Si0010008 Si0011018 Si0012001 Si0020004 Si0030001 Si0100056 Si0101021 "
    "Si0102002 Si0110006 Si0200011 Si0201002 Si0210001 Si1000025 Si1010003 "
    "Si1100006 Si1200001 Si2000001 Sk0000060 Sk0001035 Sk0002026 Sk0010010 "
    "Sk0011010 Sk0020006 Sk0021002 Sk0030001 Sk0100007 Sk0101018 Sk0102002 "
    "Sk0110002 Sk0200025 Sk0201002 Sk1000019 Sk1010008 Sk1020001 Sk1100003 "
    "Sk1200001 Sk2000001 Sl0000027 Sl0001054 Sl0010054 Sp0000214 Sp0001058 "
    "Sp0003001 Sp0010072 Sp0011021 Sp0012001 Sp0020016 Sp0021001 Sp0030002 "
    "Sp0100022 Sp0101007 Sp0102001 Sp0110004 Sp0111001 Sp0120001 Sp0200025 "
    "Sp0201001 Sp0210001 Sp0300001 Sp1000020 Sp1001002 Sp1010006 Sp1020002 "
    "Sp1100005 Sp1200002 Sp2000001 Ub0000216 Ub0001054 Ub0010054 Ud0000032 "
    "Ud0001012 Ud0002023 Ud0010070 Ud0011020 Ud0012002 Ud0020017 Ud0030001 "
    "Ud0100061 Ud0101013 Ud0102001 Ud0110004 Ud0200026 Ud0210001 Ud0300002 "
    "Ud1000011 Ud1001002 Ud1010005 Ud1020002 Ud1100006 Ud1200002 Ud2000002 "
    "Ue0000025 Ue0001066 Ue0002014 Ue0003001 Ue0010005 Ue0011005 Ue0012002 "
    "Ue0020013 Ue0030001 Ue0100032 Ue0101016 Ue0102001 Ue0110006 Ue0111002 "
    "Ue0120002 Ue0200004 Ue0300002 Ue1000022 Ue1001002 Ue1020001 Ue1100001 "
    "Ue1200001 Ue2000002 Uf0000223 Uf0001078 Uf0010001 Uf0011023 Uf0012002 "
    "Uf0020023 Uf0030002 Uf0100039 Uf0101025 Uf0102001 Uf0110006 Uf0120001 "
    "Uf0200020 Uf0201001 Uf0300001 Uf1000001 Uf1010005 Uf1020002 Uf1100008 "
    "Uf1200001 Uk0000061 Uk0001015 Uk0002006 Uk0010014 Uk0011008 Uk0020003 "
    "Uk0100019 Uk0101007 Uk0110002 Uk0200005 Uk1010001 Uk1100002 Ea0001054 "
    "Ea0010054 Eb0000081 Eb0001054 Eb0010027 Eb0100054 "
)

CERT_L7_R0 = (
    "Sa0000014 Sa0001008 Sa0002024 Sa0003023 Sa0010008 Sa0011024 Sa0020074 "
    "Sa0100074 Sa0101056 Sa0102004 Sa0110069 Sa0200017 Sa1000012 Sa1001006 "
    "Sa1010080 Sa1100024 Sb0000029 Sb0001074 Sb0002054 Sb0003041 Sb0010030 "
    "Sb0011034 Sb0012032 Sb0020017 Sb0100023 Sb0101054 Sb0102066 Sb0110010 "
    "Sb0111048 Sb0200066 Sb0201042 Sb1000077 Sb1001003 Sb1010062 Sb1100037 "
    "Sc0000046 Sc0001061 Sc0002005 Sc0003003 Sc0010041 Sc0011075 Sc0020038 "
    "Sc0100022 Sc0101050 Sc0102029 Sc0110007 Sc0200079 Sc0210040 Sc1000031 "
    "Sc1001076 Sc1010067 Sc1100038 Sd0000011 Sd0001068 Sd0002030 Sd0010017 "
    "Sd0011072 Sd0020010 Sd0100005 Sd0101030 Sd0102042 Sd0110016 Sd0200052 "
    "Sd1000004 Sd1001072 Sd1010078 Sd1100072 Se0000079 Se0001075 Se0002024 "
    "Se0003061 Se0010055 Se0011072 Se0020033 Se0100036 Se0101030 Se0102045 "
    "Se0110019 Se0111018 Se0200034 Se0201034 Se1000021 Se1001034 Se1010045 "
    "Sf0000073 Sf0001074 Sf0010043 Sf0011066 Sf0020018 Sf0100041 Sf0101077 "
    "Sf0110023 Sf0200020 Sf1000072 Sf1010045 Sf1100053 Sh0100032 Si0000003 "
    "Si0001054 Si0002041 Si0003040 Si0010079 Si0011056 Si0020059 Si0100075 "
    "Si0101010 Si0102033 Si0110025 Si0200036 Si1000024 Si1001019 Si1010007 "
    "Si1100032 Sj0000017 Sj0001062 Sj0002079 Sj0003051 Sj0010070 Sj0011007 "
    "Sj0012056 Sj0020039 Sj0100074 Sj0101007 Sj0102039 Sj0110016 Sj0200014 "
    "Sj1000035 Sj1001037 Sj1010033 Sj1100067 Sk0000020 Sk0001058 Sk0002030 "
    "Sk0010053 Sk0011018 Sk0020026 Sk0100020 Sk0101078 Sk0102039 Sk0200033 "
    "Sk1000030 Sk1010049 Sk1100049 Sl0001074 Sl0002043 Sl0010075 Sl0011004 "
    "Sl0020009 Sl0100068 Sl0101062 Sl0110026 Sl0200041 Sl1000077 Sl1010018 "
    "Sl1100080 Sm0000070 Sn0100073 Sp0000035 Sp0001031 Sp0002018 Sp0010040 "
    "Sp0011064 Sp0020030 Sp0100058 Sp0101015 Sp0102063 Sp0110080 Sp0200078 "
    "Sp0210049 Sp1000062 Sp1001029 Sp1010042 Sp1100005 Sq0100068 Sr0000064 "
    "Sr0001049 Sr0011066 Sr0020060 Sr0100004 Sr0101021 Sr0110033 Sr0200010 "
    "Sr0210073 Sr1000015 Su0100003 Sw0100007 Sx0000066 Ua0000055 Ua0010064 "
    "Ua0011051 Ua0020051 Ua0100066 Ua0101074 Ua0110065 Ua0200027 Ua1000057 "
    "Ua1010054 Ua1100026 Ub0000075 Ub0001056 Ub0010072 Ub0011007 Ub0020075 "
    "Ub0100019 Ub0101016 Ub0110017 Ub0200060 Ub1000056 Ub1010024 Ub1100011 "
    "Uc0000025 Uc0001004 Uc0002048 Uc0010046 Uc0011052 Uc0020060 Uc0021035 "
    "Uc0100069 Uc0101002 Uc0102036 Uc0110031 Uc0200040 Uc0201042 Uc1000036 "
    "Uc1010018 Uc1100065 Ud0000027 Ud0001023 Ud0010059 Ud0011078 Ud0020062 "
    "Ud0100035 Ud0101031 Ud0200005 Ud1000036 Ud1010071 Ud1100058 Ue0000025 "
    "Ue0001056 Ue0010022 Ue0011026 Ue0020059 Ue0100036 Ue0101060 Ue0200026 "
    "Ue1100074 Uf0000022 Uf0001058 Uf0010019 Uf0011012 Uf0020075 Uf0100037 "
    "Uf0101047 Uf0200070 Uf1002067 Ug0201017 Ug1011009 Ug1020022 Ug2000078 "
    "Ug3000063 Uh0000029 Uh0002002 Uh0100041 Uh1002047 Ui1101019 Ui2000018 "
    "Ui3000028 Uj0002073 Uj0010010 Uj0100042 Uj0102067 Uj1002047 Uk1011079 "
    "Uk1101013 Uk2000047 Ul0000072 Ul0002028 Ul0030020 Ul0100022 Ul0102027 "
    "Ul1002015 Ul3000029 Um0201073 Um1101029 Um3000005 Un0000033 Un0010005 "
    "Uo1011039 Uo1101047 Uo2000038 Uo3000038 Up0000051 Up0002078 Up0010007 "
    "Up0100073 Up0102024 Up3000073 Uq1011013 Uq1101001 Uq2000011 Ur0000037 "
    "Ur0002073 Ur0100061 Ut0000048 Ut0002061 Ut0010078 Uu1011021 Uu1101039 "
    "Uu2000053 Uu3000018 Uw0201052 Uw1011070 Uw1101067 Uw2000072 Uw3000019 "
    "Ux0000022 Ux0002056 Ux0010002 Ux0100036 Ux0102051 Ux1000029 Ux1001029 "
    "Ux1010029 Ux1011029 Ux1020029 Ux1100029 Ux1101029 Ux1110029 Ux1200029 "
    "Ux2000029 Ux2001029 Ux2010029 Ux2100029 Ea0000029 Ea0001029 Ea0002029 "
    "Ea0003029 Ea0010029 Ea0011029 Ea0012029 Ea0020029 Ea0021029 Ea0030029 "
    "Ea0100029 Ea0101029 Ea0102029 Ea0110029 Ea0111029 Ea0120029 Ea0200029 "
    "Ea0210029 Ea0300029 Ea1000029 Ea1001029 Ea1002029 Ea1010029 Ea1011058 "
    "Ea1100029 Ea1110029 Ea1200029 Ea2010029 Ea2100029 Eb0000048 Eb0001029 "
    "Eb0002002 Eb0003029 Eb0010030 Eb0011029 Eb0012029 Eb0020029 Eb0021029 "
    "Eb0100028 Eb0101029 Eb0110029 Eb0111029 Eb0120029 Eb0200029 Eb0201029 "
    "Eb0210029 Eb0300029 Eb1000029 Eb1001029 Eb1010029 Eb1011029 Eb1020029 "
    "Eb1100029 Eb1101029 Eb1110029 Eb1200029 Eb2000029 Eb2001029 Eb2010029 "
    "Eb2100029 Ec0000029 Ec0001029 Ec0002029 Ec0003029 Ec0010029 Ec0011029 "
    "Ec0012029 Ec0020029 Ec0021029 Ec0030029 Ec0100029 Ec0101029 Ec0102029 "
    "Ec0110029 Ec0111029 Ec0120029 Ec0200029 Ec0201044 Ec0210029 Ec0300029 "
    "Ec1000029 Ec1001029 Ec1002029 Ec1010029 Ec1011007 Ec1100029 Ec1101067 "
    "Ec1110029 Ec1200029 Ec2000009 Ec2010029 Ec2100029 Ec3000006 Ed0000016 "
    "Ed0001029 Ed0002036 Ed0003029 Ed0010030 Ed0011029 Ed0012029 Ed0020029 "
    "Ed0021029 Ed0100039 Ed0101029 Ed0110029 Ed0111029 Ed0120029 Ed0200029 "
    "Ed0201029 Ed0210029 Ed0300029 Ed1000029 Ed1001029 Ed1010029 Ed1011029 "
    "Ed1020029 Ed1100029 Ed1101029 Ed1110029 Ed1200029 Ed2000029 Ed2001029 "
    "Ed2010029 Ed2100029 Ed3000029 Ee0000029 Ee0001029 Ee0002029 Ee0003029 "
    "Ee0010029 Ee0011029 Ee0012029 Ee0020029 Ee0021029 Ee0030029 Ee0100029 "
    "Ee0101029 Ee0102029 Ee0110029 Ee0111029 Ee0120029 Ee0200029 Ee0210029 "
    "Ee0300029 Ee1000029 Ee1001029 Ee1002029 Ee1010029 Ee1100029 Ee1110029 "
    "Ee1200029 Ee2010029 Ee2100029 Ef0000062 Ef0001029 Ef0003029 Ef0010003 "
    "Ef0011029 Ef0012029 Ef0020029 Ef0021029 Ef0100031 Ef0101029 Ef0110029 "
    "Ef0111029 Ef0120029 Ef0200029 Ef0201029 Ef0210029 Ef0300029 Ef1000029 "
    "Ef1001029 Ef1010029 Ef1011029 Ef1020029 Ef1100029 Ef1101029 Ef1110029 "
    "Ef1200029 Ef2000029 Ef2001029 Ef2010029 Ef2100029 Eg0000029 Eg0001029 "
    "Eg0002029 Eg0003029 Eg0010029 Eg0011029 Eg0012029 Eg0020029 Eg0021029 "
    "Eg0030029 Eg0100029 Eg0101029 Eg0102029 Eg0110029 Eg0111029 Eg0120029 "
    "Eg0200029 Eg0210029 Eg0300029 Eg1000029 Eg1001029 Eg1002029 Eg1010029 "
    "Eg1100029 Eg1110029 Eg1200029 Eg2010029 Eg2100029 Eh0000015 Eh0001029 "
    "Eh0003029 Eh0010023 Eh0011029 Eh0012029 Eh0020029 Eh0021029 Eh0101029 "
    "Eh0110029 Eh0111029 Eh0120029 Eh0200029 Eh0201029 Eh0210029 Eh0300029 "
    "Eh1000029 Eh1001029 Eh1010029 Eh1011029 Eh1020029 Eh1100029 Eh1101029 "
    "Eh1110029 Eh1200029 Eh2000029 Eh2001029 Eh2010029 Eh2100029 Ei0000029 "
    "Ei0001029 Ei0002029 Ei0003029 Ei0010029 Ei0011029 Ei0012029 Ei0020029 "
    "Ei0021029 Ei0030029 Ei0100029 Ei0101029 Ei0102029 Ei0110029 Ei0111029 "
    "Ei0120029 Ei0200029 Ei0201003 Ei0210029 Ei0300029 Ei1000029 Ei1001029 "
    "Ei1002029 Ei1010029 Ei1011054 Ei1100029 Ei1101031 Ei1110029 Ei1200029 "
    "Ei2000073 Ei2010029 Ei2100029 Ei3000031 Ej0000013 Ej0001029 Ej0002050 "
    "Ej0003029 Ej0010077 Ej0011029 Ej0012029 Ej0020029 Ej0021029 Ej0100031 "
    "Ej0101029 Ej0102076 Ej0110029 Ej0111029 Ej0120029 Ej0200029 Ej0201029 "
    "Ej0210029 Ej0300029 Ej1000029 Ej1001029 Ej1010029 Ej1011029 Ej1020029 "
    "Ej1100029 Ej1101029 Ej1110029 Ej1200029 Ej2000029 Ej2001029 Ej2010029 "
    "Ej2100029 Ek0000029 Ek0001029 Ek0002029 Ek0003029 Ek0010029 Ek0011029 "
    "Ek0012029 Ek0020029 Ek0021029 Ek0030029 Ek0100029 Ek0101029 Ek0102029 "
    "Ek0110029 Ek0111029 Ek0120029 Ek0200029 Ek0210029 Ek0300029 Ek1000029 "
    "Ek1001029 Ek1002029 Ek1010029 Ek1011047 Ek1100029 Ek1110029 Ek1200029 "
    "Ek2000067 Ek2010029 Ek2100029 Ek3000009 El0000024 El0001029 El0002059 "
    "El0003029 El0010061 El0011029 El0012029 El0020029 El0021029 El0101029 "
    "El0102012 El0110029 El0111029 El0120029 El0200029 El0201029 El0210029 "
    "El0300029 El1000029 El1001029 El1010029 El1011029 El1020029 El1100029 "
    "El1101029 El1110029 El1200029 El2000029 El2001029 El2010029 El2100029 "
    "Em0000029 Em0001029 Em0002029 Em0003029 Em0010029 Em0011029 Em0012029 "
    "Em0020029 Em0021029 Em0030029 Em0100029 Em0101029 Em0102029 Em0110029 "
    "Em0111029 Em0120029 Em0200029 Em0210029 Em0300029 Em1000029 Em1001029 "
    "Em1002029 Em1010029 Em1100029 Em1101069 Em1110029 Em1200029 Em2000059 "
    "Em2010029 Em2100029 En0000046 En0001029 En0002042 En0003029 En0010025 "
    "En0011029 En0012029 En0020029 En0021029 En0100069 En0101029 En0102025 "
    "En0110029 En0111029 En0120029 En0200029 En0201029 En0210029 En0300029 "
    "En1000029 En1001029 En1010029 En1011029 En1020029 En1100029 En1101029 "
    "En1110029 En1200029 En2000029 En2001029 En2010029 En2100029 En3000069 "
    "Eo0000029 Eo0001029 Eo0002029 Eo0003029 Eo0010029 Eo0011029 Eo0012029 "
    "Eo0020029 Eo0021029 Eo0030029 Eo0100029 Eo0101029 Eo0102029 Eo0110029 "
    "Eo0111029 Eo0120029 Eo0200029 Eo0201022 Eo0210029 Eo0300029 Eo1000029 "
    "Eo1001029 Eo1002029 Eo1010029 Eo1011028 Eo1100029 Eo1101079 Eo1110029 "
    "Eo1200029 Eo2000048 Eo2010029 Eo2100029 Eo3000028 Ep0000058 Ep0001029 "
    "Ep0002014 Ep0003029 Ep0010002 Ep0011029 Ep0012029 Ep0020029 Ep0021029 "
    "Ep0100030 Ep0101029 Ep0102002 Ep0110029 Ep0111029 Ep0120029 Ep0200029 "
    "Ep0201029 Ep0210029 Ep0300029 Ep1000029 Ep1001029 Ep1010029 Ep1011029 "
    "Ep1020029 Ep1100029 Ep1101029 Ep1110029 Ep1200029 Ep2000029 Ep2001029 "
    "Ep2010029 Ep2100029 Ep3000012 Eq0000029 Eq0001029 Eq0002029 Eq0003029 "
    "Eq0010029 Eq0011029 Eq0012029 Eq0020029 Eq0021029 Eq0030029 Eq0100029 "
    "Eq0101029 Eq0102029 Eq0110029 Eq0111029 Eq0120029 Eq0200029 Eq0210029 "
    "Eq0300029 Eq1000029 Eq1001029 Eq1002029 Eq1010029 Eq1100029 Eq1110029 "
    "Eq1200029 Eq2000059 Eq2010029 Eq2100029 Er0000012 Er0001029 Er0003029 "
    "Er0010027 Er0011029 Er0012029 Er0020029 Er0021029 Er0100040 Er0101029 "
    "Er0110029 Er0111029 Er0120029 Er0200029 Er0201029 Er0210029 Er0300029 "
    "Er1000029 Er1001029 Er1010029 Er1011029 Er1020029 Er1100029 Er1101029 "
    "Er1110029 Er1200029 Er2000029 Er2001029 Er2010029 Er2100029 Es0000029 "
    "Es0001029 Es0002029 Es0003029 Es0010029 Es0011029 Es0012029 Es0020029 "
    "Es0021029 Es0030029 Es0100029 Es0101029 Es0102029 Es0110029 Es0111029 "
    "Es0120029 Es0200029 Es0210029 Es0300029 Es1000029 Es1001029 Es1002029 "
    "Es1010029 Es1100029 Es1110029 Es1200029 Es2010029 Es2100029 Et0000065 "
    "Et0001029 Et0003029 Et0010069 Et0011029 Et0012029 Et0020017 Et0021018 "
    "Et0101018 Et0110018 Et0111018 Et0120018 Et0200018 Et0201018 Et0210018 "
    "Et0300018 Et1000018 Et1001018 Et1010018 Et1011018 Et1020018 Et1100018 "
    "Et1101018 Et1110018 Et1200018 Et2000018 Et2001018 Et2010018 Et2100018 "
    "Eu0000018 Eu0001018 Eu0002018 Eu0003018 Eu0010018 Eu0011018 Eu0012018 "
    "Eu0020018 Eu0021018 Eu0030018 Eu0100018 Eu0101018 Eu0102018 Eu0110018 "
    "Eu0111018 Eu0120018 Eu0200018 Eu0201019 Eu0210018 Eu0300018 Eu1000018 "
    "Eu1001018 Eu1002018 Eu1010018 Eu1011025 Eu1100018 Eu1110018 Eu1200018 "
    "Eu2000064 Eu2001064 Eu2010018 Eu2100018 Eu3000076 Ev0000075 Ev0001018 "
    "Ev0002049 Ev0003018 Ev0010062 Ev0011018 Ev0012018 Ev0020018 Ev0021018 "
    "Ev0100004 Ev0101018 Ev0102056 Ev0110018 Ev0111018 Ev0120018 Ev0200018 "
    "Ev0201018 Ev0210018 Ev0300018 Ev1000018 Ev1001018 Ev1002053 Ev1010018 "
    "Ev1011018 Ev1020018 Ev1100018 Ev1101018 Ev1110018 Ev1200018 Ev2000018 "
    "Ev2001018 Ev2010018 Ev2100018 Ev3000029 Ew0000018 Ew0001018 Ew0002018 "
    "Ew0003018 Ew0010037 Ew0011037 Ew0012037 Ew0020037 Ew0021037 Ew0030037 "
    "Ew0100037 Ew0101037 Ew0102037 Ew0110037 Ew0111037 Ew0120037 Ew0200043 "
    "Ew0210043 Ew0300043 Ew1000022 Ew1001022 Ew1002022 Ew1010026 Ew1100061 "
    "Ew1110061 Ew1200061 Ew2010061 Ew2100061 Ex0000046 Ex0001061 Ex0002036 "
    "Ex0003061 Ex0010040 Ex0011061 Ex0012061 Ex0020061 Ex0021061 Ex0100020 "
    "Ex0101061 Ex0102075 Ex0110061 Ex0111061 Ex0120061 Ex0200061 Ex0201061 "
    "Ex0210061 Ex0300061 Ex1000061 Ex1001061 Ex1010061 Ex1011061 Ex1020061 "
    "Ex1100061 Ex1101061 Ex1110061 Ex1200061 Ex2000061 Ex2001061 Ex2010061 "
    "Ex2100061 Ex3000068 "
)

CERT_L7_R1 = (
    "Sa0000050 Sa0001072 Sa0002073 Sa0003053 Sa0010069 Sa0011080 Sa0020050 "
    "Sa0100064 Sa0101033 Sa0102005 Sa0110009 Sa0200015 Sa1000078 Sa1001057 "
    "Sa1010027 Sb0000036 Sb0001068 Sb0003002 Sb0010022 Sb0011047 Sb0020041 "
    "Sb0100037 Sb0101009 Sb0102013 Sb0110030 Sb0200009 Sb0201059 Sb1000027 "
    "Sb1001017 Sb1010065 Sb1100007 Sc0000003 Sc0001014 Sc0002025 Sc0003012 "
    "Sc0010078 Sc0011030 Sc0020074 Sc0100050 Sc0101056 Sc0102057 Sc0110014 "
    "Sc0200037 Sc1000021 Sc1001019 Sc1010026 Sc1100025 Sd0000066 Sd0001019 "
    "Sd0002025 Sd0003064 Sd0010051 Sd0011075 Sd0012063 Sd0020062 Sd0100003 "
    "Sd0101047 Sd0102039 Sd0110059 Sd0200046 Sd1001041 Sd1010029 Sd1100004 "
    "Se0000050 Se0001031 Se0002022 Se0003054 Se0010080 Se0011026 Se0020079 "
    "Se0100060 Se0101066 Se0102049 Se0110005 Se0200063 Se0201027 Se1000051 "
    "Se1001078 Se1010033 Se1100048 Sf0000004 Sf0001075 Sf0010044 Sf0011013 "
    "Sf0020016 Sf0100075 Sf0101030 Sf0200027 Sf1000041 Sf1010013 Sf1100071 "
    "Si0000042 Si0001014 Si0002073 Si0003046 Si0010066 Si0011042 Si0012066 "
    "Si0020012 Si0100016 Si0101058 Si0102067 Si0110011 Si0200009 Si1000077 "
    "Si1001012 Si1010014 Si1100010 Sj0000063 Sj0001056 Sj0002014 Sj0003008 "
    "Sj0010063 Sj0011042 Sj0012037 Sj0020062 Sj0100004 Sj0101012 Sj0102038 "
    "Sj0110020 Sj0200060 Sj1000057 Sj1001065 Sj1010080 Sj1100041 Sk0000005 "
    "Sk0001037 Sk0002062 Sk0010038 Sk0011022 Sk0020011 Sk0100057 Sk0101068 "
    "Sk0110015 Sk0200036 Sk1000046 Sk1010056 Sk1100007 Sl0000006 Sl0001065 "
    "Sl0002017 Sl0011070 Sl0020026 Sl0100041 Sl0101010 Sl0110061 Sl0200060 "
    "Sl1000015 Sl1010078 Sl1100027 Sm0000002 Sn0100004 Sp0000019 Sp0001072 "
    "Sp0002010 Sp0010076 Sp0011009 Sp0020009 Sp0100060 Sp0101057 Sp0110043 "
    "Sp0200003 Sp1000064 Sp1001066 Sp1010037 Sp1100019 Sp1101076 Sq0100054 "
    "Sr0000007 Sr0001036 Sr0010023 Sr0011076 Sr0020069 Sr0100031 Sr0101043 "
    "Sr0110058 Sr0200027 Sr0201076 Sr1000020 Sr1101068 Su0100038 Sw0100019 "
    "Sx0000071 Ua0000079 Ua0010042 Ua0011021 Ua0020007 Ua0101030 Ua0110027 "
    "Ua0200048 Ua1000063 Ua1010001 Ua1100026 Ub0000003 Ub0001004 Ub0010060 "
    "Ub0011064 Ub0020022 Ub0100046 Ub0101016 Ub0110021 Ub0200060 Ub1000030 "
    "Ub1100027 Uc0000025 Uc0001009 Uc0002004 Uc0010043 Uc0011035 Uc0020001 "
    "Uc0100044 Uc0101072 Uc0102032 Uc0110067 Uc0200035 Uc0201063 Uc1000036 "
    "Uc1010055 Uc1100080 Uc1101032 Ud0000074 Ud0001055 Ud0010035 Ud0011067 "
    "Ud0020068 Ud0100007 Ud0101027 Ud0200063 Ud1000013 Ud1010069 Ue0000067 "
    "Ue0001035 Ue0010055 Ue0011043 Ue0020074 Ue0100066 Ue0101033 Ue0200057 "
    "Ue1101021 Uf0000049 Uf0001067 Uf0002028 Uf0010055 Uf0011039 Uf0020021 "
    "Uf0030066 Uf0100072 Uf0101067 Uf1002073 Ug0201036 Ug1020051 Ug1101057 "
    "Ug2000039 Ug2001045 Ug3000075 Uh0002064 Uh0100042 Uh0102045 Ui1101050 "
    "Ui2000047 Ui3000046 Uj0002055 Uj0100018 Uj0102016 Uj1002028 Uk1011055 "
    "Uk1101003 Uk2000034 Uk3000066 Ul0000047 Ul0002079 Ul0100013 Ul0102058 "
    "Ul1002057 Um0201067 Um1101007 Un0000053 Un0002008 Un0010020 Uo1011071 "
    "Uo1101070 Uo2000075 Uo3000059 Up0000058 Up0002026 Up0010013 Up0100031 "
    "Uq1011037 Uq1101071 Uq2000066 Uq3000049 Ur0000061 Ur0002031 Ur0010040 "
    "Ur0100005 Us2000060 Ut0000018 Ut0002071 Ut0010026 Uu1011040 Uu1101006 "
    "Uu2000040 Uu3000076 Uw0201021 Uw1011043 Uw1101079 Uw2000040 Uw3000025 "
    "Ux0000059 Ux0002009 Ux0010025 Ux0100062 Ux0102047 Ux0200016 Ux0201016 "
    "Ux0210016 Ux0300016 Ux1000032 Ux1001032 Ux1010027 Ux1011027 Ux1020027 "
    "Ux1100027 Ux1101027 Ux1110027 Ux1200027 Ux2000027 Ux2001027 Ux2010027 "
    "Ux2100027 Ea0000027 Ea0001027 Ea0002027 Ea0003027 Ea0010027 Ea0011027 "
    "Ea0012027 Ea0020027 Ea0021027 Ea0030027 Ea0100027 Ea0101027 Ea0102027 "
    "Ea0110027 Ea0111027 Ea0120027 Ea0200027 Ea0210027 Ea0300027 Ea1000027 "
    "Ea1001027 Ea1002027 Ea1010027 Ea1011018 Ea1100027 Ea1101063 Ea1110027 "
    "Ea1200027 Ea2010027 Ea2100027 Eb0000018 Eb0001027 Eb0002062 Eb0003027 "
    "Eb0010072 Eb0011027 Eb0012027 Eb0020027 Eb0021027 Eb0100056 Eb0101027 "
    "Eb0110027 Eb0111027 Eb0120027 Eb0200027 Eb0201027 Eb0210027 Eb0300027 "
    "Eb1000027 Eb1001027 Eb1010027 Eb1011027 Eb1020027 Eb1100027 Eb1101027 "
    "Eb1110027 Eb1200027 Eb2000027 Eb2001027 Eb2010027 Eb2100027 Ec0000027 "
    "Ec0001027 Ec0002027 Ec0003027 Ec0010027 Ec0011027 Ec0012027 Ec0020027 "
    "Ec0021027 Ec0030027 Ec0100027 Ec0101027 Ec0102027 Ec0110027 Ec0111027 "
    "Ec0120027 Ec0200027 Ec0201049 Ec0210027 Ec0300027 Ec1000027 Ec1001027 "
    "Ec1002027 Ec1010027 Ec1011063 Ec1100027 Ec1101029 Ec1110027 Ec1200027 "
    "Ec2010027 Ec2100027 Ed0000015 Ed0001027 Ed0002008 Ed0003027 Ed0010049 "
    "Ed0011027 Ed0012027 Ed0020027 Ed0021027 Ed0100026 Ed0101027 Ed0102036 "
    "Ed0110027 Ed0111027 Ed0120027 Ed0200027 Ed0201027 Ed0210027 Ed0300027 "
    "Ed1000027 Ed1001027 Ed1010027 Ed1011027 Ed1020027 Ed1100027 Ed1101027 "
    "Ed1110027 Ed1200027 Ed2000027 Ed2001027 Ed2010027 Ed2100027 Ee0000027 "
    "Ee0001027 Ee0002027 Ee0003027 Ee0010027 Ee0011027 Ee0012027 Ee0020027 "
    "Ee0021027 Ee0030027 Ee0100027 Ee0101027 Ee0102027 Ee0110027 Ee0111027 "
    "Ee0120027 Ee0200027 Ee0210027 Ee0300027 Ee1000027 Ee1001027 Ee1002027 "
    "Ee1010027 Ee1100027 Ee1110027 Ee1200027 Ee2010027 Ee2100027 Ef0000024 "
    "Ef0001027 Ef0003027 Ef0010035 Ef0011027 Ef0012027 Ef0020027 Ef0021027 "
    "Ef0100043 Ef0101027 Ef0110027 Ef0111027 Ef0120027 Ef0200027 Ef0201027 "
    "Ef0210027 Ef0300027 Ef1000027 Ef1001027 Ef1010027 Ef1011027 Ef1020027 "
    "Ef1100027 Ef1101027 Ef1110027 Ef1200027 Ef2000027 Ef2001027 Ef2010027 "
    "Ef2100027 Eg0000027 Eg0001027 Eg0002027 Eg0003027 Eg0010027 Eg0011027 "
    "Eg0012027 Eg0020027 Eg0021027 Eg0030027 Eg0100027 Eg0101027 Eg0102027 "
    "Eg0110027 Eg0111027 Eg0120027 Eg0200027 Eg0210027 Eg0300027 Eg1000027 "
    "Eg1001027 Eg1002027 Eg1010027 Eg1100027 Eg1110027 Eg1200027 Eg2010027 "
    "Eg2100027 Eh0000055 Eh0001027 Eh0003027 Eh0010051 Eh0011027 Eh0012027 "
    "Eh0020027 Eh0021027 Eh0100079 Eh0101027 Eh0110027 Eh0111027 Eh0120027 "
    "Eh0200027 Eh0201027 Eh0210027 Eh0300027 Eh1000027 Eh1001027 Eh1010027 "
    "Eh1011027 Eh1020027 Eh1100027 Eh1101027 Eh1110027 Eh1200027 Eh2000027 "
    "Eh2001027 Eh2010027 Eh2100027 Ei0000027 Ei0001027 Ei0002027 Ei0003027 "
    "Ei0010027 Ei0011027 Ei0012027 Ei0020027 Ei0021027 Ei0030027 Ei0100027 "
    "Ei0101027 Ei0102027 Ei0110027 Ei0111027 Ei0120027 Ei0200027 Ei0201052 "
    "Ei0210027 Ei0300027 Ei1000027 Ei1001027 Ei1002027 Ei1010027 Ei1011042 "
    "Ei1100027 Ei1101065 Ei1110027 Ei1200027 Ei2000029 Ei2010027 Ei2100027 "
    "Ei3000055 Ej0000056 Ej0001027 Ej0002064 Ej0003027 Ej0010040 Ej0011027 "
    "Ej0012027 Ej0020027 Ej0021027 Ej0100022 Ej0101027 Ej0102051 Ej0110027 "
    "Ej0111027 Ej0120027 Ej0200027 Ej0201027 Ej0210027 Ej0300027 Ej1000027 "
    "Ej1001027 Ej1002065 Ej1010027 Ej1011027 Ej1020027 Ej1100027 Ej1101027 "
    "Ej1110027 Ej1200027 Ej2000027 Ej2001027 Ej2010027 Ej2100027 Ek0000027 "
    "Ek0001027 Ek0002027 Ek0003027 Ek0010027 Ek0011027 Ek0012027 Ek0020027 "
    "Ek0021027 Ek0030027 Ek0100027 Ek0101027 Ek0102027 Ek0110027 Ek0111027 "
    "Ek0120027 Ek0200027 Ek0210027 Ek0300027 Ek1000027 Ek1001027 Ek1002027 "
    "Ek1010027 Ek1100027 Ek1101062 Ek1110027 Ek1200027 Ek2000072 Ek2010027 "
    "Ek2100027 Ek3000016 El0000075 El0001027 El0002071 El0003027 El0010001 "
    "El0011027 El0012027 El0020027 El0021027 El0100055 El0101027 El0102019 "
    "El0110027 El0111027 El0120027 El0200027 El0201027 El0210027 El0300027 "
    "El1000027 El1001027 El1010027 El1011027 El1020027 El1100027 El1101027 "
    "El1110027 El1200027 El2000027 El2001027 El2010027 El2100027 Em0000027 "
    "Em0001027 Em0002027 Em0003027 Em0010027 Em0011027 Em0012027 Em0020027 "
    "Em0021027 Em0030027 Em0100027 Em0101027 Em0102027 Em0110027 Em0111027 "
    "Em0120027 Em0200027 Em0201039 Em0210027 Em0300027 Em1000027 Em1001027 "
    "Em1002027 Em1010027 Em1100027 Em1101062 Em1110027 Em1200027 Em2000062 "
    "Em2010027 Em2100027 En0000039 En0001027 En0002045 En0003027 En0010026 "
    "En0011027 En0012027 En0020027 En0021027 En0100021 En0101027 En0102012 "
    "En0110027 En0111027 En0120027 En0200027 En0201027 En0210027 En0300027 "
    "En1000027 En1001027 En1002057 En1010027 En1011027 En1020027 En1100027 "
    "En1101027 En1110027 En1200027 En2000027 En2001027 En2010027 En2100027 "
    "En3000062 Eo0000027 Eo0001027 Eo0002027 Eo0003027 Eo0010027 Eo0011027 "
    "Eo0012027 Eo0020027 Eo0021027 Eo0030027 Eo0100027 Eo0101027 Eo0102027 "
    "Eo0110027 Eo0111027 Eo0120027 Eo0200027 Eo0201020 Eo0210027 Eo0300027 "
    "Eo1000027 Eo1001027 Eo1002027 Eo1010027 Eo1011033 Eo1100027 Eo1101051 "
    "Eo1110027 Eo1200027 Eo2000025 Eo2010027 Eo2100027 Eo3000031 Ep0000041 "
    "Ep0001027 Ep0002059 Ep0003027 Ep0010052 Ep0011027 Ep0012027 Ep0020027 "
    "Ep0021027 Ep0100011 Ep0101027 Ep0102042 Ep0110027 Ep0111027 Ep0120027 "
    "Ep0200027 Ep0201027 Ep0210027 Ep0300027 Ep1000027 Ep1001027 Ep1002036 "
    "Ep1010027 Ep1011027 Ep1020027 Ep1100027 Ep1101027 Ep1110027 Ep1200027 "
    "Ep2000027 Ep2001027 Ep2010027 Ep2100027 Ep3000002 Eq0000027 Eq0001027 "
    "Eq0002027 Eq0003027 Eq0010027 Eq0011027 Eq0012027 Eq0020027 Eq0021027 "
    "Eq0030027 Eq0100027 Eq0101027 Eq0102027 Eq0110027 Eq0111027 Eq0120027 "
    "Eq0200027 Eq0210027 Eq0300027 Eq1000027 Eq1001027 Eq1002027 Eq1010027 "
    "Eq1100027 Eq1110027 Eq1200027 Eq2000030 Eq2010027 Eq2100027 Er0000006 "
    "Er0001027 Er0002054 Er0003027 Er0010023 Er0011027 Er0012027 Er0020027 "
    "Er0021027 Er0100002 Er0101027 Er0110027 Er0111027 Er0120027 Er0200027 "
    "Er0201027 Er0210027 Er0300027 Er1000027 Er1001027 Er1010027 Er1011027 "
    "Er1020027 Er1100027 Er1101027 Er1110027 Er1200027 Er2000027 Er2001027 "
    "Er2010027 Er2100027 Es0000027 Es0001027 Es0002027 Es0003027 Es0010027 "
    "Es0011027 Es0012027 Es0020027 Es0021027 Es0030027 Es0100027 Es0101027 "
    "Es0102027 Es0110027 Es0111027 Es0120027 Es0200027 Es0210027 Es0300027 "
    "Es1000027 Es1001027 Es1002027 Es1010027 Es1100027 Es1110027 Es1200027 "
    "Es2010027 Es2100027 Et0000008 Et0001027 Et0003027 Et0010007 Et0011063 "
    "Et0012063 Et0020036 Et0021027 Et0100079 Et0101027 Et0110027 Et0111027 "
    "Et0120027 Et0200027 Et0201027 Et0210027 Et0300027 Et1000027 Et1001027 "
    "Et1010027 Et1011027 Et1020027 Et1100027 Et1101027 Et1110027 Et1200027 "
    "Et2000027 Et2001027 Et2010027 Et2100027 Eu0000027 Eu0001027 Eu0002027 "
    "Eu0003027 Eu0010027 Eu0011027 Eu0012027 Eu0020027 Eu0021027 Eu0030027 "
    "Eu0100027 Eu0101027 Eu0102027 Eu0110027 Eu0111027 Eu0120027 Eu0200027 "
    "Eu0201039 Eu0210027 Eu0300027 Eu1000027 Eu1001027 Eu1002027 Eu1010027 "
    "Eu1011010 Eu1100027 Eu1101018 Eu1110027 Eu1200027 Eu2000030 Eu2001008 "
    "Eu2010027 Eu2100027 Eu3000068 Ev0000059 Ev0001027 Ev0002037 Ev0003027 "
    "Ev0010080 Ev0011027 Ev0012027 Ev0020027 Ev0021027 Ev0100042 Ev0101027 "
    "Ev0102030 Ev0110027 Ev0111027 Ev0120027 Ev0200027 Ev0201027 Ev0210027 "
    "Ev0300027 Ev1000027 Ev1001027 Ev1002066 Ev1010027 Ev1011027 Ev1020027 "
    "Ev1100027 Ev1101027 Ev1110027 Ev1200027 Ev2000027 Ev2001027 Ev2010027 "
    "Ev2100027 Ev3000049 Ew0000027 Ew0001027 Ew0002027 Ew0003027 Ew0010019 "
    "Ew0011019 Ew0012019 Ew0020019 Ew0021019 Ew0030019 Ew0100019 Ew0101019 "
    "Ew0102019 Ew0110019 Ew0111019 Ew0120019 Ew0200015 Ew0210015 Ew0300015 "
    "Ew1000045 Ew1001051 Ew1002051 Ew1010035 Ew1100015 Ew1110015 Ew1200015 "
    "Ew2010015 Ew2100015 Ex0000036 Ex0001015 Ex0002013 Ex0003015 Ex0010057 "
    "Ex0011015 Ex0012015 Ex0020015 Ex0021015 Ex0100063 Ex0101015 Ex0102073 "
    "Ex0110015 Ex0111015 Ex0120015 Ex0200015 Ex0201015 Ex0210015 Ex0300015 "
    "Ex1000015 Ex1001015 Ex1002080 Ex1010015 Ex1011015 Ex1020015 Ex1100015 "
    "Ex1101015 Ex1110015 Ex1200015 Ex2000015 Ex2001015 Ex2010015 Ex2100015 "
    "Ex3000017 "
)

CERT_L7_R2 = (
    "Sa0000006 Sa0001006 Sa0002024 Sa0010021 Sa0011007 Sa0020014 Sa0100006 "
    "Sa0101019 Sa0200011 Sa1000018 Sb0000018 Sb0001002 Sb0002025 Sb0010009 "
    "Sb0011015 Sb0020022 Sb0100005 Sb0101007 Sb0200008 Sb1000020 Sc0000007 "
    "Sc0001024 Sc0002010 Sc0010021 Sc0011021 Sc0100018 Sc0101015 Sc0110007 "
    "Sc0200005 Sc1000021 Sd0000020 Sd0001016 Sd0002001 Sd0010006 Sd0011020 "
    "Sd0100021 Sd0101015 Sd0110024 Sd0200017 Sd1000021 Se0000006 Se0001001 "
    "Se0002007 Se0010005 Se0011019 Se0020002 Se0100018 Se0101017 Se0110017 "
    "Se1000012 Sf0000004 Sf0001020 Sf0010024 Sf0100026 Sf0101001 Sf1000011 "
    "Si0000017 Si0001009 Si0002008 Si0010010 Si0011022 Si0020008 Si0100021 "
    "Si0101006 Si0110008 Si0200008 Si1000026 Sj0000007 Sj0001022 Sj0002003 "
    "Sj0010020 Sj0011010 Sj0020001 Sj0100007 Sj0101014 Sj0110009 Sj0200011 "
    "Sj1000008 Sk0000001 Sk0001012 Sk0010006 Sk0020016 Sk0100011 Sk0101023 "
    "Sk0200022 Sk1000015 Sl0000009 Sl0001002 Sl0010002 Sl0100023 Sl1000004 "
    "Sp0000014 Sp0001005 Sp0002009 Sp0010012 Sp0011025 Sp0020006 Sp0100003 "
    "Sp0101019 Sp0200016 Sp1000021 Sr0000023 Sr0001020 Sr0010026 Sr0011025 "
    "Sr0020018 Sr0100019 Sr0101014 Ua0000008 Ua0010025 Ua0100015 Ua0101026 "
    "Ua0200018 Ua1000026 Ub0000020 Ub0001010 Ub0010004 Ub1000010 Uc0000012 "
    "Uc0001007 Uc0002026 Uc0010025 Uc0011019 Uc0020020 Uc0100014 Uc0101011 "
    "Uc0200024 Uc1000002 Ud0000019 Ud0001023 Ud0010004 Ud1000007 Ue0000013 "
    "Ue0001024 Ue0010014 Uf0000016 Uf0001009 Uf0002014 Uf0010004 Ug0200007 "
    "Ug1100025 Uh0000017 Uh0100020 Uk0020011 Ul0000024 Ul0002004 Ul2000024 "
    "Um0200022 Um1001025 Um1010015 Um1100008 Uo0020012 Uo0200024 Uo1001003 "
    "Uo1010016 Up0000019 Up0002025 Up0100018 Up2000008 Uq1001011 Uq1010009 "
    "Ur0000019 Ur0002023 Ur0100001 Us0020014 Us1010021 Ut0000014 Ut0002016 "
    "Ut2000025 Uu0020003 Uu1010013 Uw0200012 Uw1001017 Uw1010001 Ux0000022 "
    "Ux0001014 Ux0002008 Ux0010014 Ux0011014 Ux0020014 Ux0100025 Ux0101014 "
    "Ux0200014 Ux1000013 Ux1001013 Ux1010013 Ux1100013 Ux2000023 Ea0000013 "
    "Ea0001013 Ea0002013 Ea0010013 Ea0011013 Ea0100013 Ea0101013 Ea0110013 "
    "Ea1000013 Ea2000013 Eb0000021 Eb0001013 Eb0010013 Eb0011013 Eb0020013 "
    "Eb0100013 Eb0101013 Eb0200013 Eb1000013 Eb1001013 Eb1010013 Eb1100013 "
    "Eb2000008 Ec0000013 Ec0001013 Ec0002013 Ec0010013 Ec0011013 Ec0020019 "
    "Ec0100013 Ec0101013 Ec0110013 Ec0200007 Ec1000013 Ec1001024 Ec1010016 "
    "Ec1100019 Ec2000013 Ed0000004 Ed0001013 Ed0002019 Ed0010013 Ed0011013 "
    "Ed0020013 Ed0100020 Ed0101013 Ed0200013 Ed1000013 Ed1001013 Ed1010013 "
    "Ed1100013 Ed2000012 Ee0000013 Ee0001013 Ee0002013 Ee0010013 Ee0011013 "
    "Ee0100013 Ee0101013 Ee0110013 Ee1000013 Ee2000013 Ef0000023 Ef0001013 "
    "Ef0010013 Ef0011013 Ef0020013 Ef0101013 Ef0200013 Ef1000013 Ef1001013 "
    "Ef1010013 Ef1100013 Eg0000013 Eg0001013 Eg0002013 Eg0010013 Eg0011013 "
    "Eg0100013 Eg0101013 Eg0110013 Eg1000013 Eg2000013 Eh0000025 Eh0001013 "
    "Eh0010013 Eh0011013 Eh0020013 Eh0101013 Eh0200013 Eh1000013 Eh1001013 "
    "Eh1010013 Eh1100013 Ei0000013 Ei0001013 Ei0002013 Ei0010013 Ei0011013 "
    "Ei0020025 Ei0100013 Ei0101013 Ei0110013 Ei0200023 Ei1000013 Ei1100003 "
    "Ei2000013 Ej0000012 Ej0001013 Ej0010013 Ej0011013 Ej0020013 Ej0100004 "
    "Ej0101013 Ej0200013 Ej1000013 Ej1001013 Ej1010013 Ej1100013 Ej2000019 "
    "Ek0000013 Ek0001013 Ek0002013 Ek0010013 Ek0011013 Ek0100013 Ek0101013 "
    "Ek0110013 Ek1000013 Ek1010011 Ek2000013 El0000007 El0001013 El0002017 "
    "El0010013 El0011013 El0020013 El0100014 El0101013 El0200013 El1000013 "
    "El1001013 El1010013 El1100013 El2000014 Em0000013 Em0001013 Em0002013 "
    "Em0010013 Em0011013 Em0020014 Em0100013 Em0101013 Em0110013 Em0200001 "
    "Em1000013 Em1001004 Em1010016 Em1100024 Em2000013 En0000011 En0001013 "
    "En0002025 En0010013 En0011013 En0020013 En0100020 En0101013 En0200013 "
    "En1000013 En1001013 En1010013 En1100013 En2000026 Eo0000013 Eo0001013 "
    "Eo0002013 Eo0010013 Eo0011013 Eo0020013 Eo0100013 Eo0101013 Eo0110013 "
    "Eo0200021 Eo1000013 Eo1001014 Eo1010006 Eo1100014 Eo2000013 Ep0000026 "
    "Ep0001013 Ep0002012 Ep0010013 Ep0011013 Ep0020013 Ep0100007 Ep0101013 "
    "Ep0200013 Ep1000013 Ep1001013 Ep1010013 Ep1100013 Ep2000013 Eq0000013 "
    "Eq0001013 Eq0002013 Eq0010013 Eq0011013 Eq0100013 Eq0101013 Eq0110013 "
    "Eq1000013 Eq2000013 Er0000025 Er0001013 Er0010013 Er0011013 Er0020013 "
    "Er0100017 Er0101013 Er0200013 Er1000013 Er1001013 Er1010013 Er1100013 "
    "Es0000013 Es0001013 Es0002013 Es0010013 Es0011013 Es0100013 Es0101013 "
    "Es0110013 Es1000013 Es2000013 Et0000003 Et0001013 Et0010007 Et0011006 "
    "Et0020006 Et0101006 Et0200006 Et1000006 Et1001006 Et1010006 Et1100006 "
    "Eu0000006 Eu0001006 Eu0002006 Eu0010006 Eu0011006 Eu0020002 Eu0100006 "
    "Eu0101006 Eu0110006 Eu0200007 Eu1000006 Eu1010009 Eu1100023 Eu2000006 "
    "Ev0000019 Ev0001006 Ev0002015 Ev0010006 Ev0011006 Ev0020006 Ev0100022 "
    "Ev0101006 Ev0200006 Ev1000006 Ev1001006 Ev1010006 Ev1100006 Ew0000025 "
    "Ew0001025 Ew0002025 Ew0010025 Ew0011025 Ew0100025 Ew0101025 Ew0110025 "
    "Ew1000023 Ew2000023 Ex0000009 Ex0001023 Ex0010023 Ex0011023 Ex0020023 "
    "Ex0100006 Ex0101023 Ex0200023 Ex1000023 Ex1001023 Ex1010023 Ex1100023 "
    "Ex2000010 "
)

CERT_L13_R0 = (
    "Sa0000030 Sa0001080 Sa0002004 Sa0003021 Sa0010019 Sa0011029 Sa0020009 "
    "Sa0100080 Sa0101048 Sa0102046 Sa0110001 Sa0200039 Sa1000078 Sa1001034 "
    "Sa1010018 Sa1100054 Sb0000005 Sb0001060 Sb0002014 Sb0003064 Sb0010025 "
    "Sb0011036 Sb0012002 Sb0020033 Sb0100031 Sb0101040 Sb0102065 Sb0110043 "
    "Sb0111072 Sb0200055 Sb0201079 Sb1000057 Sb1001069 Sb1010035 Sb1100058 "
    "Sc0000057 Sc0001050 Sc0002009 Sc0003056 Sc0010066 Sc0011004 Sc0020039 "
    "Sc0100044 Sc0101027 Sc0102033 Sc0110063 Sc0200049 Sc0210036 Sc1000075 "
    "Sc1001068 Sc1010008 Sc1100034 Sd0000076 Sd0001072 Sd0002069 Sd0010002 "
    "Sd0011076 Sd0020047 Sd0100075 Sd0101045 Sd0102011 Sd0110011 Sd0200039 "
    "Sd1000049 Sd1001022 Sd1010008 Sd1100018 Se0000075 Se0001015 Se0002010 "
    "Se0003036 Se0010078 Se0011042 Se0020049 Se0100008 Se0101055 Se0102078 "
    "Se0110068 Se0111071 Se0200065 Se0201056 Se1000043 Se1001036 Se1010052 "
    "Se1100048 Sf0000024 Sf0001079 Sf0010072 Sf0011006 Sf0020030 Sf0100063 "
    "Sf0101074 Sf0110078 Sf0200061 Sf1000049 Sf1010037 Sf1100046 Sh0100053 "
    "Si0000050 Si0001019 Si0002013 Si0003025 Si0010062 Si0011027 Si0020060 "
    "Si0100054 Si0101056 Si0102012 Si0110016 Si0200001 Si1000036 Si1001049 "
    "Si1010077 Si1100044 Sj0000068 Sj0001011 Sj0002039 Sj0003079 Sj0010004 "
    "Sj0011007 Sj0012030 Sj0020030 Sj0100041 Sj0101055 Sj0102039 Sj0110001 "
    "Sj0200078 Sj1000018 Sj1001033 Sj1010065 Sj1100077 Sk0000021 Sk0001068 "
    "Sk0002028 Sk0010059 Sk0011019 Sk0020053 Sk0100031 Sk0101043 Sk0102050 "
    "Sk0110055 Sk0200062 Sk1000038 Sk1010079 Sk1100005 Sl0000026 Sl0001050 "
    "Sl0002024 Sl0010035 Sl0011077 Sl0020075 Sl0100010 Sl0101011 Sl0110015 "
    "Sl0200027 Sl1000072 Sl1010015 Sl1100018 Sm0000070 Sn0100063 Sp0000012 "
    "Sp0001039 Sp0002050 Sp0010074 Sp0011063 Sp0020023 Sp0100047 Sp0101045 "
    "Sp0102027 Sp0110078 Sp0200025 Sp0210019 Sp1000023 Sp1001015 Sp1010031 "
    "Sp1100056 Sq0100022 Sr0000033 Sr0001034 Sr0010049 Sr0011012 Sr0020080 "
    "Sr0100068 Sr0101001 Sr0110053 Sr0200033 Sr0210002 Sr1000071 Su0100042 "
    "Sw0100037 Sx0000010 Ua0000034 Ua0010038 Ua0011030 Ua0020030 Ua0100060 "
    "Ua0101050 Ua0110019 Ua0200075 Ua1000057 Ua1010010 Ua1100071 Ub0000009 "
    "Ub0001079 Ub0010078 Ub0011045 Ub0020048 Ub0100041 Ub0101053 Ub0110008 "
    "Ub0200057 Ub1000030 Ub1010054 Ub1100045 Uc0000068 Uc0001017 Uc0002062 "
    "Uc0010045 Uc0011017 Uc0020048 Uc0021019 Uc0100078 Uc0101058 Uc0102047 "
    "Uc0110049 Uc0200032 Uc0201051 Uc1000030 Uc1010064 Uc1100080 Ud0000012 "
    "Ud0001020 Ud0010041 Ud0011039 Ud0020072 Ud0100012 Ud0101007 Ud0200020 "
    "Ud1000053 Ud1010073 Ud1100078 Ue0000080 Ue0001045 Ue0010021 Ue0011074 "
    "Ue0020030 Ue0100046 Ue0101027 Ue0200029 Ue1100080 Uf0000007 Uf0001050 "
    "Uf0010031 Uf0011049 Uf0020016 Uf0100072 Uf0200005 Uf1002077 Ug0201063 "
    "Ug1011030 Ug1020039 Ug2000076 Ug3000054 Uh0000037 Uh0002073 Uh0100063 "
    "Uh1002052 Ui1101079 Ui2000022 Ui3000001 Uj0002073 Uj0010056 Uj0100021 "
    "Uj0102025 Uj1002010 Uk1011048 Uk1101002 Uk2000078 Ul0000042 Ul0002078 "
    "Ul0030027 Ul0100046 Ul0102066 Ul1002005 Ul3000065 Um0201047 Um3000035 "
    "Un0000028 Un0010078 Uo1011022 Uo1101039 Uo2000041 Uo3000023 Up0000037 "
    "Up0002068 Up0010014 Up0100033 Up0102016 Up3000073 Uq1011044 Uq1101041 "
    "Uq2000052 Uq3000031 Ur0000070 Ur0002077 Ur0100010 Ut0000020 Ut0002063 "
    "Ut0010018 Uu1011002 Uu1101032 Uu2000014 Uu3000027 Uw0201045 Uw1011045 "
    "Uw1101046 Uw2000054 Uw3000053 Ux0000028 Ux0002044 Ux0010013 Ux0100064 "
    "Ux0102041 Ux1000045 Ux1001045 Ux1010045 Ux1011045 Ux1020045 Ux1100045 "
    "Ux1101045 Ux1110045 Ux1200045 Ux2000045 Ux2001045 Ux2010045 Ux2100045 "
    "Ea0000045 Ea0001045 Ea0002045 Ea0003045 Ea0010045 Ea0011045 Ea0012045 "
    "Ea0020045 Ea0021045 Ea0030045 Ea0100045 Ea0101045 Ea0102045 Ea0110045 "
    "Ea0111045 Ea0120045 Ea0200045 Ea0210045 Ea0300045 Ea1000045 Ea1001045 "
    "Ea1002045 Ea1010045 Ea1011019 Ea1100045 Ea1110045 Ea1200045 Ea2010045 "
    "Ea2100045 Eb0000075 Eb0001045 Eb0002076 Eb0003045 Eb0010003 Eb0011045 "
    "Eb0012045 Eb0020045 Eb0021045 Eb0100065 Eb0101045 Eb0110045 Eb0111045 "
    "Eb0120045 Eb0200045 Eb0201045 Eb0210045 Eb0300045 Eb1000045 Eb1001045 "
    "Eb1010045 Eb1011045 Eb1020045 Eb1100045 Eb1101045 Eb1110045 Eb1200045 "
    "Eb2000045 Eb2001045 Eb2010045 Eb2100045 Ec0000045 Ec0001045 Ec0002045 "
    "Ec0003045 Ec0010045 Ec0011045 Ec0012045 Ec0020045 Ec0021045 Ec0030045 "
    "Ec0100045 Ec0101045 Ec0102045 Ec0110045 Ec0111045 Ec0120045 Ec0200045 "
    "Ec0201071 Ec0210045 Ec0300045 Ec1000045 Ec1001045 Ec1002045 Ec1010045 "
    "Ec1011041 Ec1100045 Ec1101077 Ec1110045 Ec1200045 Ec2000060 Ec2010045 "
    "Ec2100045 Ec3000057 Ed0000033 Ed0001045 Ed0002023 Ed0003045 Ed0010037 "
    "Ed0011045 Ed0012045 Ed0020045 Ed0021045 Ed0100041 Ed0101045 Ed0110045 "
    "Ed0111045 Ed0120045 Ed0200045 Ed0201045 Ed0210045 Ed0300045 Ed1000045 "
    "Ed1001045 Ed1010045 Ed1011045 Ed1020045 Ed1100045 Ed1101045 Ed1110045 "
    "Ed1200045 Ed2000045 Ed2001045 Ed2010045 Ed2100045 Ed3000037 Ee0000045 "
    "Ee0001045 Ee0002045 Ee0003045 Ee0010045 Ee0011045 Ee0012045 Ee0020045 "
    "Ee0021045 Ee0030045 Ee0100045 Ee0101045 Ee0102045 Ee0110045 Ee0111045 "
    "Ee0120045 Ee0200045 Ee0210045 Ee0300045 Ee1000045 Ee1001045 Ee1002045 "
    "Ee1010045 Ee1100045 Ee1110045 Ee1200045 Ee2010045 Ee2100045 Ef0000036 "
    "Ef0001045 Ef0003045 Ef0010011 Ef0011045 Ef0012045 Ef0020045 Ef0021045 "
    "Ef0100034 Ef0101045 Ef0110045 Ef0111045 Ef0120045 Ef0200045 Ef0201045 "
    "Ef0210045 Ef0300045 Ef1000045 Ef1001045 Ef1010045 Ef1011045 Ef1020045 "
    "Ef1100045 Ef1101045 Ef1110045 Ef1200045 Ef2000045 Ef2001045 Ef2010045 "
    "Ef2100045 Eg0000045 Eg0001045 Eg0002045 Eg0003045 Eg0010045 Eg0011045 "
    "Eg0012045 Eg0020045 Eg0021045 Eg0030045 Eg0100045 Eg0101045 Eg0102045 "
    "Eg0110045 Eg0111045 Eg0120045 Eg0200045 Eg0210045 Eg0300045 Eg1000045 "
    "Eg1001045 Eg1002045 Eg1010045 Eg1100045 Eg1110045 Eg1200045 Eg2010045 "
    "Eg2100045 Eh0000041 Eh0001045 Eh0003045 Eh0010062 Eh0011045 Eh0012045 "
    "Eh0020045 Eh0021045 Eh0101045 Eh0110045 Eh0111045 Eh0120045 Eh0200045 "
    "Eh0201045 Eh0210045 Eh0300045 Eh1000045 Eh1001045 Eh1010045 Eh1011045 "
    "Eh1020045 Eh1100045 Eh1101045 Eh1110045 Eh1200045 Eh2000045 Eh2001045 "
    "Eh2010045 Eh2100045 Ei0000045 Ei0001045 Ei0002045 Ei0003045 Ei0010045 "
    "Ei0011045 Ei0012045 Ei0020045 Ei0021045 Ei0030045 Ei0100045 Ei0101045 "
    "Ei0102045 Ei0110045 Ei0111045 Ei0120045 Ei0200045 Ei0201046 Ei0210045 "
    "Ei0300045 Ei1000045 Ei1001045 Ei1002045 Ei1010045 Ei1011072 Ei1100045 "
    "Ei1101007 Ei1110045 Ei1200045 Ei2000017 Ei2010045 Ei2100045 Ei3000036 "
    "Ej0000076 Ej0001045 Ej0002055 Ej0003045 Ej0010076 Ej0011045 Ej0012045 "
    "Ej0020045 Ej0021045 Ej0100048 Ej0101045 Ej0102016 Ej0110045 Ej0111045 "
    "Ej0120045 Ej0200045 Ej0201045 Ej0210045 Ej0300045 Ej1000045 Ej1001045 "
    "Ej1010045 Ej1011045 Ej1020045 Ej1100045 Ej1101045 Ej1110045 Ej1200045 "
    "Ej2000045 Ej2001045 Ej2010045 Ej2100045 Ek0000045 Ek0001045 Ek0002045 "
    "Ek0003045 Ek0010045 Ek0011045 Ek0012045 Ek0020045 Ek0021045 Ek0030045 "
    "Ek0100045 Ek0101045 Ek0102045 Ek0110045 Ek0111045 Ek0120045 Ek0200045 "
    "Ek0210045 Ek0300045 Ek1000045 Ek1001045 Ek1002045 Ek1010045 Ek1011076 "
    "Ek1100045 Ek1110045 Ek1200045 Ek2000065 Ek2010045 Ek2100045 Ek3000036 "
    "El0000060 El0001045 El0002009 El0003045 El0010045 El0011045 El0012045 "
    "El0020045 El0021045 El0101045 El0102032 El0110045 El0111045 El0120045 "
    "El0200045 El0201045 El0210045 El0300045 El1000045 El1001045 El1010045 "
    "El1011045 El1020045 El1100045 El1101045 El1110045 El1200045 El2000045 "
    "El2001045 El2010045 El2100045 Em0000045 Em0001045 Em0002045 Em0003045 "
    "Em0010045 Em0011045 Em0012045 Em0020045 Em0021045 Em0030045 Em0100045 "
    "Em0101045 Em0102045 Em0110045 Em0111045 Em0120045 Em0200045 Em0201015 "
    "Em0210045 Em0300045 Em1000045 Em1001045 Em1002045 Em1010045 Em1011063 "
    "Em1100045 Em1101008 Em1110045 Em1200045 Em2000050 Em2010045 Em2100045 "
    "En0000016 En0001045 En0002047 En0003045 En0010011 En0011045 En0012045 "
    "En0020045 En0021045 En0100030 En0101045 En0102029 En0110045 En0111045 "
    "En0120045 En0200045 En0201045 En0210045 En0300045 En1000045 En1001045 "
    "En1010045 En1011045 En1020045 En1100045 En1101045 En1110045 En1200045 "
    "En2000045 En2001045 En2010045 En2100045 En3000017 Eo0000045 Eo0001045 "
    "Eo0002045 Eo0003045 Eo0010045 Eo0011045 Eo0012045 Eo0020045 Eo0021045 "
    "Eo0030045 Eo0100045 Eo0101045 Eo0102045 Eo0110045 Eo0111045 Eo0120045 "
    "Eo0200045 Eo0210045 Eo0300045 Eo1000045 Eo1001045 Eo1002045 Eo1010045 "
    "Eo1011047 Eo1100045 Eo1101034 Eo1110045 Eo1200045 Eo2000021 Eo2010045 "
    "Eo2100045 Eo3000012 Ep0000005 Ep0001045 Ep0002054 Ep0003045 Ep0010055 "
    "Ep0011045 Ep0012045 Ep0020045 Ep0021045 Ep0100020 Ep0101045 Ep0102006 "
    "Ep0110045 Ep0111045 Ep0120045 Ep0200045 Ep0201045 Ep0210045 Ep0300045 "
    "Ep1000045 Ep1001045 Ep1010045 Ep1011045 Ep1020045 Ep1100045 Ep1101045 "
    "Ep1110045 Ep1200045 Ep2000045 Ep2001045 Ep2010045 Ep2100045 Ep3000006 "
    "Eq0000045 Eq0001045 Eq0002045 Eq0003045 Eq0010045 Eq0011045 Eq0012045 "
    "Eq0020045 Eq0021045 Eq0030045 Eq0100045 Eq0101045 Eq0102045 Eq0110045 "
    "Eq0111045 Eq0120045 Eq0200045 Eq0210045 Eq0300045 Eq1000045 Eq1001045 "
    "Eq1002045 Eq1010045 Eq1100045 Eq1110045 Eq1200045 Eq2000009 Eq2010045 "
    "Eq2100045 Er0000012 Er0001045 Er0002048 Er0003045 Er0010038 Er0011045 "
    "Er0012045 Er0020045 Er0021045 Er0100035 Er0101045 Er0110045 Er0111045 "
    "Er0120045 Er0200045 Er0201045 Er0210045 Er0300045 Er1000045 Er1001045 "
    "Er1010045 Er1011045 Er1020045 Er1100045 Er1101045 Er1110045 Er1200045 "
    "Er2000045 Er2001045 Er2010045 Er2100045 Es0000045 Es0001045 Es0002045 "
    "Es0003045 Es0010045 Es0011045 Es0012045 Es0020045 Es0021045 Es0030045 "
    "Es0100045 Es0101045 Es0102045 Es0110045 Es0111045 Es0120045 Es0200045 "
    "Es0210045 Es0300045 Es1000045 Es1001045 Es1002045 Es1010045 Es1100045 "
    "Es1110045 Es1200045 Es2010045 Es2100045 Et0000006 Et0001045 Et0003045 "
    "Et0010059 Et0011045 Et0012045 Et0020063 Et0021072 Et0100076 Et0101072 "
    "Et0110072 Et0111072 Et0120072 Et0200072 Et0201072 Et0210072 Et0300072 "
    "Et1000072 Et1001072 Et1010072 Et1011072 Et1020072 Et1100072 Et1101072 "
    "Et1110072 Et1200072 Et2000072 Et2001072 Et2010072 Et2100072 Eu0000072 "
    "Eu0001072 Eu0002072 Eu0003072 Eu0010072 Eu0011072 Eu0012072 Eu0020072 "
    "Eu0021072 Eu0030072 Eu0100072 Eu0101072 Eu0102072 Eu0110072 Eu0111072 "
    "Eu0120072 Eu0200072 Eu0201071 Eu0210072 Eu0300072 Eu1000072 Eu1001072 "
    "Eu1002072 Eu1010072 Eu1011051 Eu1100072 Eu1101076 Eu1110072 Eu1200072 "
    "Eu2000071 Eu2001077 Eu2010072 Eu2100072 Eu3000014 Ev0000056 Ev0001072 "
    "Ev0002038 Ev0003072 Ev0010074 Ev0011072 Ev0012072 Ev0020072 Ev0021072 "
    "Ev0100078 Ev0101072 Ev0102045 Ev0110072 Ev0111072 Ev0120072 Ev0200072 "
    "Ev0201072 Ev0210072 Ev0300072 Ev1000072 Ev1001072 Ev1002018 Ev1010072 "
    "Ev1011072 Ev1020072 Ev1100072 Ev1101072 Ev1110072 Ev1200072 Ev2000072 "
    "Ev2001072 Ev2010072 Ev2100072 Ev3000013 Ew0000072 Ew0001072 Ew0002072 "
    "Ew0003072 Ew0010004 Ew0011004 Ew0012004 Ew0020004 Ew0021004 Ew0030004 "
    "Ew0100004 Ew0101004 Ew0102004 Ew0110004 Ew0111004 Ew0120004 Ew0200033 "
    "Ew0210033 Ew0300033 Ew1000039 Ew1001039 Ew1002039 Ew1010005 Ew1100054 "
    "Ew1110054 Ew1200054 Ew2010054 Ew2100054 Ex0000058 Ex0001054 Ex0002055 "
    "Ex0003054 Ex0010056 Ex0011054 Ex0012054 Ex0020054 Ex0021054 Ex0100020 "
    "Ex0101054 Ex0102061 Ex0110054 Ex0111054 Ex0120054 Ex0200054 Ex0201054 "
    "Ex0210054 Ex0300054 Ex1000054 Ex1001054 Ex1010054 Ex1011054 Ex1020054 "
    "Ex1100054 Ex1101054 Ex1110054 Ex1200054 Ex2000054 Ex2001054 Ex2010054 "
    "Ex2100054 Ex3000014 "
)

CERT_L13_R1 = (
    "Sa0000021 Sa0001075 Sa0002057 Sa0003064 Sa0010056 Sa0011033 Sa0012065 "
    "Sa0020052 Sa0100040 Sa0101006 Sa0102021 Sa0110027 Sa0200079 Sa1000003 "
    "Sa1001038 Sa1010010 Sa1100003 Sb0000055 Sb0001010 Sb0002035 Sb0003031 "
    "Sb0010031 Sb0011053 Sb0020052 Sb0100080 Sb0101007 Sb0102006 Sb0110044 "
    "Sb0200057 Sb0201060 Sb1000018 Sb1001059 Sb1010012 Sb1100053 Sc0000014 "
    "Sc0001074 Sc0002016 Sc0003001 Sc0010027 Sc0011068 Sc0020058 Sc0100009 "
    "Sc0101005 Sc0102066 Sc0200041 Sc1000010 Sc1001008 Sc1010019 Sc1100025 "
    "Sd0000067 Sd0001025 Sd0002033 Sd0003046 Sd0010044 Sd0011053 Sd0012067 "
    "Sd0020028 Sd0100053 Sd0101039 Sd0102021 Sd0110014 Sd0200037 Sd1000022 "
    "Sd1001050 Sd1010063 Sd1100006 Se0000077 Se0001049 Se0002015 Se0003080 "
    "Se0010073 Se0011047 Se0020078 Se0100076 Se0101046 Se0102016 Se0110017 "
    "Se0200077 Se0201032 Se1000013 Se1001011 Se1010010 Se1100012 Sf0000012 "
    "Sf0001033 Sf0010045 Sf0011065 Sf0020062 Sf0100046 Sf0101004 Sf0200069 "
    "Sf1000048 Sf1010076 Sf1100052 Si0000005 Si0001072 Si0002037 Si0003026 "
    "Si0010047 Si0011015 Si0012010 Si0020003 Si0100079 Si0101041 Si0102023 "
    "Si0110047 Si0200029 Si1000032 Si1001001 Si1010057 Si1100031 Sj0000041 "
    "Sj0001067 Sj0002026 Sj0003011 Sj0010020 Sj0011038 Sj0012014 Sj0020033 "
    "Sj0100079 Sj0101033 Sj0102004 Sj0110060 Sj0200031 Sj1000071 Sj1001005 "
    "Sj1010034 Sj1100066 Sk0000078 Sk0001002 Sk0002072 Sk0010053 Sk0011074 "
    "Sk0020005 Sk0100036 Sk0101080 Sk0110044 Sk0200057 Sk1000078 Sk1010032 "
    "Sk1100077 Sl0000010 Sl0001047 Sl0002077 Sl0010047 Sl0011058 Sl0020019 "
    "Sl0100074 Sl0101075 Sl0110021 Sl0200037 Sl1000007 Sl1010051 Sl1100010 "
    "Sm0000055 Sn0100047 Sp0000048 Sp0001024 Sp0002048 Sp0011062 Sp0020041 "
    "Sp0100061 Sp0101043 Sp0110069 Sp0200006 Sp1000014 Sp1001038 Sp1010074 "
    "Sp1100017 Sp1101001 Sq0100041 Sr0000031 Sr0001013 Sr0010012 Sr0011001 "
    "Sr0020013 Sr0100073 Sr0101043 Sr0110080 Sr0200044 Sr0201023 Sr1000024 "
    "Sr1101053 Su0100067 Sw0100002 Sx0000069 Ua0000026 Ua0010005 Ua0011018 "
    "Ua0020033 Ua0100003 Ua0101072 Ua0110069 Ua0200012 Ua1000020 Ua1010074 "
    "Ua1100069 Ub0000012 Ub0001012 Ub0010074 Ub0011056 Ub0020030 Ub0100016 "
    "Ub0101070 Ub0110067 Ub0200021 Ub1000019 Ub1010003 Ub1100052 Uc0000050 "
    "Uc0001041 Uc0002077 Uc0010052 Uc0011080 Uc0020042 Uc0100071 Uc0101063 "
    "Uc0102051 Uc0110008 Uc0200005 Uc0201072 Uc1000013 Uc1010040 Uc1100010 "
    "Uc1101051 Ud0000028 Ud0001053 Ud0011006 Ud0020050 Ud0100015 Ud0101068 "
    "Ud0200071 Ud1000014 Ud1010078 Ue0000055 Ue0001045 Ue0010021 Ue0011049 "
    "Ue0020080 Ue0100014 Ue0101006 Ue0200047 Ue1101032 Uf0000080 Uf0001043 "
    "Uf0002066 Uf0010033 Uf0011063 Uf0020009 Uf0030068 Uf0100020 Uf0101037 "
    "Uf0200057 Uf1002071 Ug0201076 Ug1020023 Ug1101020 Ug2000036 Ug2001049 "
    "Ug3000024 Uh0002028 Uh0100004 Uh0102049 Ui1101078 Ui2000002 Ui3000054 "
    "Uj0002007 Uj0100017 Uj0102064 Uj1002066 Uk1011043 Uk1101068 Uk2000004 "
    "Uk3000064 Ul0000023 Ul0002062 Ul0100027 Ul0102020 Ul1002025 Um0201049 "
    "Um1101022 Un0000030 Un0002079 Un0010033 Uo1011007 Uo1101044 Uo2000023 "
    "Uo3000069 Up0000079 Up0002018 Up0010014 Up0100037 Uq1011069 Uq1101011 "
    "Uq2000047 Uq3000028 Ur0000004 Ur0002054 Ur0010026 Ur0100066 Us2000027 "
    "Ut0000080 Ut0002074 Ut0010008 Uu1011055 Uu1101037 Uu2000012 Uu3000029 "
    "Uw0201038 Uw1011077 Uw1101025 Uw2000020 Uw3000044 Ux0000059 Ux0002073 "
    "Ux0010038 Ux0100063 Ux0102061 Ux0200075 Ux0201075 Ux0210075 Ux0300075 "
    "Ux1000051 Ux1001051 Ux1010034 Ux1011034 Ux1020034 Ux1100034 Ux1101034 "
    "Ux1110034 Ux1200034 Ux2000034 Ux2001034 Ux2010034 Ux2100034 Ea0000034 "
    "Ea0001034 Ea0002034 Ea0003034 Ea0010034 Ea0011034 Ea0012034 Ea0020034 "
    "Ea0021034 Ea0030034 Ea0100034 Ea0101034 Ea0102034 Ea0110034 Ea0111034 "
    "Ea0120034 Ea0200034 Ea0210034 Ea0300034 Ea1000034 Ea1001034 Ea1002034 "
    "Ea1010034 Ea1011017 Ea1100034 Ea1101006 Ea1110034 Ea1200034 Ea2010034 "
    "Ea2100034 Eb0000035 Eb0001034 Eb0002033 Eb0003034 Eb0010055 Eb0011034 "
    "Eb0012034 Eb0020034 Eb0021034 Eb0100080 Eb0101034 Eb0110034 Eb0111034 "
    "Eb0120034 Eb0200034 Eb0201034 Eb0210034 Eb0300034 Eb1000034 Eb1001034 "
    "Eb1010034 Eb1011034 Eb1020034 Eb1100034 Eb1101034 Eb1110034 Eb1200034 "
    "Eb2000034 Eb2001034 Eb2010034 Eb2100034 Ec0000034 Ec0001034 Ec0002034 "
    "Ec0003034 Ec0010034 Ec0011034 Ec0012034 Ec0020034 Ec0021034 Ec0030034 "
    "Ec0100034 Ec0101034 Ec0102034 Ec0110034 Ec0111034 Ec0120034 Ec0200034 "
    "Ec0201051 Ec0210034 Ec0300034 Ec1000034 Ec1001034 Ec1002034 Ec1010034 "
    "Ec1011029 Ec1100034 Ec1101051 Ec1110034 Ec1200034 Ec2010034 Ec2100034 "
    "Ed0000064 Ed0001034 Ed0002016 Ed0003034 Ed0010056 Ed0011034 Ed0012034 "
    "Ed0020034 Ed0021034 Ed0100080 Ed0101034 Ed0102032 Ed0110034 Ed0111034 "
    "Ed0120034 Ed0200034 Ed0201034 Ed0210034 Ed0300034 Ed1000034 Ed1001034 "
    "Ed1010034 Ed1011034 Ed1020034 Ed1100034 Ed1101034 Ed1110034 Ed1200034 "
    "Ed2000034 Ed2001034 Ed2010034 Ed2100034 Ee0000034 Ee0001034 Ee0002034 "
    "Ee0003034 Ee0010034 Ee0011034 Ee0012034 Ee0020034 Ee0021034 Ee0030034 "
    "Ee0100034 Ee0101034 Ee0102034 Ee0110034 Ee0111034 Ee0120034 Ee0200034 "
    "Ee0210034 Ee0300034 Ee1000034 Ee1001034 Ee1002034 Ee1010034 Ee1100034 "
    "Ee1110034 Ee1200034 Ee2010034 Ee2100034 Ef0000006 Ef0001034 Ef0003034 "
    "Ef0010002 Ef0011034 Ef0012034 Ef0020034 Ef0021034 Ef0100073 Ef0101034 "
    "Ef0110034 Ef0111034 Ef0120034 Ef0200034 Ef0201034 Ef0210034 Ef0300034 "
    "Ef1000034 Ef1001034 Ef1010034 Ef1011034 Ef1020034 Ef1100034 Ef1101034 "
    "Ef1110034 Ef1200034 Ef2000034 Ef2001034 Ef2010034 Ef2100034 Eg0000034 "
    "Eg0001034 Eg0002034 Eg0003034 Eg0010034 Eg0011034 Eg0012034 Eg0020034 "
    "Eg0021034 Eg0030034 Eg0100034 Eg0101034 Eg0102034 Eg0110034 Eg0111034 "
    "Eg0120034 Eg0200034 Eg0210034 Eg0300034 Eg1000034 Eg1001034 Eg1002034 "
    "Eg1010034 Eg1100034 Eg1110034 Eg1200034 Eg2010034 Eg2100034 Eh0000068 "
    "Eh0001034 Eh0003034 Eh0010001 Eh0011034 Eh0012034 Eh0020034 Eh0021034 "
    "Eh0100041 Eh0101034 Eh0110034 Eh0111034 Eh0120034 Eh0200034 Eh0201034 "
    "Eh0210034 Eh0300034 Eh1000034 Eh1001034 Eh1010034 Eh1011034 Eh1020034 "
    "Eh1100034 Eh1101034 Eh1110034 Eh1200034 Eh2000034 Eh2001034 Eh2010034 "
    "Eh2100034 Ei0000034 Ei0001034 Ei0002034 Ei0003034 Ei0010034 Ei0011034 "
    "Ei0012034 Ei0020034 Ei0021034 Ei0030034 Ei0100034 Ei0101034 Ei0102034 "
    "Ei0110034 Ei0111034 Ei0120034 Ei0200034 Ei0201047 Ei0210034 Ei0300034 "
    "Ei1000034 Ei1001034 Ei1002034 Ei1010034 Ei1011014 Ei1100034 Ei1101011 "
    "Ei1110034 Ei1200034 Ei2000048 Ei2010034 Ei2100034 Ei3000028 Ej0000017 "
    "Ej0001034 Ej0002048 Ej0003034 Ej0010010 Ej0011034 Ej0012034 Ej0020034 "
    "Ej0021034 Ej0100048 Ej0101034 Ej0102064 Ej0110034 Ej0111034 Ej0120034 "
    "Ej0200034 Ej0201034 Ej0210034 Ej0300034 Ej1000034 Ej1001034 Ej1002038 "
    "Ej1010034 Ej1011034 Ej1020034 Ej1100034 Ej1101034 Ej1110034 Ej1200034 "
    "Ej2000034 Ej2001034 Ej2010034 Ej2100034 Ek0000034 Ek0001034 Ek0002034 "
    "Ek0003034 Ek0010034 Ek0011034 Ek0012034 Ek0020034 Ek0021034 Ek0030034 "
    "Ek0100034 Ek0101034 Ek0102034 Ek0110034 Ek0111034 Ek0120034 Ek0200034 "
    "Ek0210034 Ek0300034 Ek1000034 Ek1001034 Ek1002034 Ek1010034 Ek1100034 "
    "Ek1101031 Ek1110034 Ek1200034 Ek2000075 Ek2010034 Ek2100034 Ek3000063 "
    "El0000010 El0001034 El0002027 El0003034 El0010035 El0011034 El0012034 "
    "El0020034 El0021034 El0100027 El0101034 El0102018 El0110034 El0111034 "
    "El0120034 El0200034 El0201034 El0210034 El0300034 El1000034 El1001034 "
    "El1010034 El1011034 El1020034 El1100034 El1101034 El1110034 El1200034 "
    "El2000034 El2001034 El2010034 El2100034 Em0000034 Em0001034 Em0002034 "
    "Em0003034 Em0010034 Em0011034 Em0012034 Em0020034 Em0021034 Em0030034 "
    "Em0100034 Em0101034 Em0102034 Em0110034 Em0111034 Em0120034 Em0200034 "
    "Em0201034 Em0210034 Em0300034 Em1000034 Em1001034 Em1002034 Em1010034 "
    "Em1100034 Em1101008 Em1110034 Em1200034 Em2000068 Em2010034 Em2100034 "
    "En0000020 En0001034 En0002071 En0003034 En0010039 En0011034 En0012034 "
    "En0020034 En0021034 En0100078 En0101034 En0102069 En0110034 En0111034 "
    "En0120034 En0200034 En0201034 En0210034 En0300034 En1000034 En1001034 "
    "En1002024 En1010034 En1011034 En1020034 En1100034 En1101034 En1110034 "
    "En1200034 En2000034 En2001034 En2010034 En2100034 En3000068 Eo0000034 "
    "Eo0001034 Eo0002034 Eo0003034 Eo0010034 Eo0011034 Eo0012034 Eo0020034 "
    "Eo0021034 Eo0030034 Eo0100034 Eo0101034 Eo0102034 Eo0110034 Eo0111034 "
    "Eo0120034 Eo0200034 Eo0201049 Eo0210034 Eo0300034 Eo1000034 Eo1001034 "
    "Eo1002034 Eo1010034 Eo1011073 Eo1100034 Eo1101033 Eo1110034 Eo1200034 "
    "Eo2000080 Eo2010034 Eo2100034 Ep0000017 Ep0001034 Ep0002052 Ep0003034 "
    "Ep0010025 Ep0011034 Ep0012034 Ep0020034 Ep0021034 Ep0100042 Ep0101034 "
    "Ep0102079 Ep0110034 Ep0111034 Ep0120034 Ep0200034 Ep0201034 Ep0210034 "
    "Ep0300034 Ep1000034 Ep1001034 Ep1002035 Ep1010034 Ep1011034 Ep1020034 "
    "Ep1100034 Ep1101034 Ep1110034 Ep1200034 Ep2000034 Ep2001034 Ep2010034 "
    "Ep2100034 Ep3000009 Eq0000034 Eq0001034 Eq0002034 Eq0003034 Eq0010034 "
    "Eq0011034 Eq0012034 Eq0020034 Eq0021034 Eq0030034 Eq0100034 Eq0101034 "
    "Eq0102034 Eq0110034 Eq0111034 Eq0120034 Eq0200034 Eq0210034 Eq0300034 "
    "Eq1000034 Eq1001034 Eq1002034 Eq1010034 Eq1100034 Eq1110034 Eq1200034 "
    "Eq2000048 Eq2010034 Eq2100034 Er0000051 Er0001034 Er0002068 Er0003034 "
    "Er0010054 Er0011034 Er0012034 Er0020034 Er0021034 Er0100004 Er0101034 "
    "Er0110034 Er0111034 Er0120034 Er0200034 Er0201034 Er0210034 Er0300034 "
    "Er1000034 Er1001034 Er1010034 Er1011034 Er1020034 Er1100034 Er1101034 "
    "Er1110034 Er1200034 Er2000034 Er2001034 Er2010034 Er2100034 Es0000034 "
    "Es0001034 Es0002034 Es0003034 Es0010034 Es0011034 Es0012034 Es0020034 "
    "Es0021034 Es0030034 Es0100034 Es0101034 Es0102034 Es0110034 Es0111034 "
    "Es0120034 Es0200034 Es0210034 Es0300034 Es1000034 Es1001034 Es1002034 "
    "Es1010034 Es1100034 Es1110034 Es1200034 Es2010034 Es2100034 Et0000080 "
    "Et0001034 Et0003034 Et0010079 Et0011051 Et0012051 Et0020076 Et0021056 "
    "Et0100078 Et0101056 Et0110056 Et0111056 Et0120056 Et0200056 Et0201056 "
    "Et0210056 Et0300056 Et1000056 Et1001056 Et1010056 Et1011056 Et1020056 "
    "Et1100056 Et1101056 Et1110056 Et1200056 Et2000056 Et2001056 Et2010056 "
    "Et2100056 Eu0000056 Eu0001056 Eu0002056 Eu0003056 Eu0010056 Eu0011056 "
    "Eu0012056 Eu0020056 Eu0021056 Eu0030056 Eu0100056 Eu0101056 Eu0102056 "
    "Eu0110056 Eu0111056 Eu0120056 Eu0200056 Eu0201048 Eu0210056 Eu0300056 "
    "Eu1000056 Eu1001056 Eu1002056 Eu1010056 Eu1011032 Eu1100056 Eu1101029 "
    "Eu1110056 Eu1200056 Eu2000014 Eu2001055 Eu2010056 Eu2100056 Eu3000060 "
    "Ev0000080 Ev0001056 Ev0002073 Ev0003056 Ev0010016 Ev0011056 Ev0012056 "
    "Ev0020056 Ev0021056 Ev0100033 Ev0101056 Ev0102005 Ev0110056 Ev0111056 "
    "Ev0120056 Ev0200056 Ev0201056 Ev0210056 Ev0300056 Ev1000056 Ev1001056 "
    "Ev1002003 Ev1010056 Ev1011056 Ev1020056 Ev1100056 Ev1101056 Ev1110056 "
    "Ev1200056 Ev2000056 Ev2001056 Ev2010056 Ev2100056 Ev3000073 Ew0000056 "
    "Ew0001056 Ew0002056 Ew0003056 Ew0010013 Ew0011013 Ew0012013 Ew0020013 "
    "Ew0021013 Ew0030013 Ew0100013 Ew0101013 Ew0102013 Ew0110013 Ew0111013 "
    "Ew0120013 Ew0200072 Ew0210072 Ew0300072 Ew1000049 Ew1001023 Ew1002023 "
    "Ew1010012 Ew1100013 Ew1110013 Ew1200013 Ew2010013 Ew2100013 Ex0000061 "
    "Ex0001013 Ex0002029 Ex0003013 Ex0010040 Ex0011013 Ex0012013 Ex0020013 "
    "Ex0021013 Ex0100001 Ex0101013 Ex0102011 Ex0110013 Ex0111013 Ex0120013 "
    "Ex0200013 Ex0201013 Ex0210013 Ex0300013 Ex1000013 Ex1001013 Ex1002037 "
    "Ex1010013 Ex1011013 Ex1020013 Ex1100013 Ex1101013 Ex1110013 Ex1200013 "
    "Ex2000013 Ex2001013 Ex2010013 Ex2100013 Ex3000050 "
)

CERT_L13_R2 = (
    "Sa0000014 Sa0001002 Sa0002015 Sa0010004 Sa0011007 Sa0020005 Sa0100018 "
    "Sa0101007 Sa0200004 Sa1000018 Sb0000024 Sb0001015 Sb0002017 Sb0010019 "
    "Sb0011015 Sb0020019 Sb0100020 Sb0101010 Sb0200025 Sb1000011 Sc0000007 "
    "Sc0001025 Sc0002025 Sc0010004 Sc0011003 Sc0020009 Sc0100026 Sc0101025 "
    "Sc0110012 Sc0200005 Sc1000015 Sd0000026 Sd0001004 Sd0002017 Sd0010025 "
    "Sd0011017 Sd0101002 Sd0110026 Sd0200006 Sd1000016 Se0000003 Se0001016 "
    "Se0010021 Se0020024 Se0100009 Se0101010 Se0110020 Se0200022 Se1000022 "
    "Sf0000011 Sf0001006 Sf0010003 Sf0100026 Sf0101012 Sf1000013 Si0000014 "
    "Si0001022 Si0002025 Si0010002 Si0011011 Si0020022 Si0101016 Si0110016 "
    "Si1000016 Sj0000002 Sj0001008 Sj0002003 Sj0010021 Sj0011006 Sj0020025 "
    "Sj0100011 Sj0101021 Sj0110009 Sj0200007 Sj1000011 Sk0000001 Sk0001014 "
    "Sk0010007 Sk0020008 Sk0100014 Sk0101004 Sk0200026 Sk1000020 Sl0000024 "
    "Sl0001015 Sl0100008 Sl1000004 Sp0000024 Sp0001013 Sp0002006 Sp0010008 "
    "Sp0011004 Sp0020021 Sp0100003 Sp0101014 Sp0200011 Sp1000022 Sr0000012 "
    "Sr0001005 Sr0010020 Sr0011021 Sr0020025 Sr0100012 Sr0101012 Ua0000004 "
    "Ua0010006 Ua0100016 Ua0101012 Ua0200004 Ua1000014 Ub0000020 Ub0001021 "
    "Ub0010021 Ub1000010 Uc0000003 Uc0001018 Uc0002004 Uc0010009 Uc0011006 "
    "Uc0020015 Uc0100006 Uc0101007 Uc0200003 Uc1000026 Ud0000021 Ud0001017 "
    "Ud0010002 Ud1000023 Ue0000009 Ue0001024 Ue0010007 Uf0000014 Uf0001010 "
    "Uf0002014 Uf0010009 Ug0200016 Ug1100013 Uh0000002 Uh0100008 Uk0020024 "
    "Ul0000024 Ul0002010 Ul2000011 Um0020001 Um0200013 Um1001009 Um1010013 "
    "Um1100025 Uo0020021 Uo0200004 Uo1001016 Uo1010016 Up0002025 Up0100008 "
    "Up2000005 Uq1001023 Uq1010001 Ur0002005 Ur0100015 Us0020020 Us1010022 "
    "Ut0000025 Ut0002008 Ut0100018 Ut2000014 Uu0020019 Uu1010006 Uw0020020 "
    "Uw0200025 Uw1001006 Uw1010009 Ux0000002 Ux0001014 Ux0002005 Ux0010014 "
    "Ux0011014 Ux0020014 Ux0100009 Ux0101014 Ux0200014 Ux1000013 Ux1001013 "
    "Ux1010013 Ux1100013 Ux2000022 Ea0000013 Ea0001013 Ea0002013 Ea0010013 "
    "Ea0011013 Ea0100013 Ea0101013 Ea0110013 Ea1000013 Ea2000013 Eb0000012 "
    "Eb0001013 Eb0010013 Eb0011013 Eb0020013 Eb0100019 Eb0101013 Eb0200013 "
    "Eb1000013 Eb1001013 Eb1010013 Eb1100013 Eb2000026 Ec0000013 Ec0001013 "
    "Ec0002013 Ec0010013 Ec0011013 Ec0020003 Ec0100013 Ec0101013 Ec0110013 "
    "Ec0200001 Ec1000013 Ec1001003 Ec1010015 Ec1100013 Ec2000013 Ed0000016 "
    "Ed0001013 Ed0002012 Ed0010013 Ed0011013 Ed0020013 Ed0100025 Ed0101013 "
    "Ed0200013 Ed1000013 Ed1001013 Ed1010013 Ed1100013 Ed2000021 Ee0000013 "
    "Ee0001013 Ee0002013 Ee0010013 Ee0011013 Ee0100013 Ee0101013 Ee0110013 "
    "Ee1000013 Ee2000013 Ef0000014 Ef0001013 Ef0010013 Ef0011013 Ef0020013 "
    "Ef0101013 Ef0200013 Ef1000013 Ef1001013 Ef1010013 Ef1100013 Eg0000013 "
    "Eg0001013 Eg0002013 Eg0010013 Eg0011013 Eg0100013 Eg0101013 Eg0110013 "
    "Eg1000013 Eg2000013 Eh0000005 Eh0001013 Eh0010013 Eh0011013 Eh0020013 "
    "Eh0101013 Eh0200013 Eh1000013 Eh1001013 Eh1010013 Eh1100013 Ei0000013 "
    "Ei0001013 Ei0002013 Ei0010013 Ei0011013 Ei0020011 Ei0100013 Ei0101013 "
    "Ei0110013 Ei0200001 Ei1000013 Ei1100002 Ei2000013 Ej0000019 Ej0001013 "
    "Ej0010013 Ej0011013 Ej0020013 Ej0100020 Ej0101013 Ej0200013 Ej1000013 "
    "Ej1001013 Ej1010013 Ej1100013 Ej2000014 Ek0000013 Ek0001013 Ek0002013 "
    "Ek0010013 Ek0011013 Ek0100013 Ek0101013 Ek0110013 Ek1000013 Ek1010015 "
    "Ek2000013 El0000020 El0001013 El0010013 El0011013 El0020013 El0100003 "
    "El0101013 El0200013 El1000013 El1001013 El1010013 El1100013 El2000014 "
    "Em0000013 Em0001013 Em0002013 Em0010013 Em0011013 Em0020019 Em0100013 "
    "Em0101013 Em0110013 Em0200012 Em1000013 Em1001012 Em1010015 Em1100006 "
    "Em2000013 En0000005 En0001013 En0002021 En0010013 En0011013 En0020013 "
    "En0100022 En0101013 En0200013 En1000013 En1001013 En1010013 En1100013 "
    "En2000011 Eo0000013 Eo0001013 Eo0002013 Eo0010013 Eo0011013 Eo0020020 "
    "Eo0100013 Eo0101013 Eo0110013 Eo0200023 Eo1000013 Eo1001003 Eo1010007 "
    "Eo1100020 Eo2000013 Ep0000008 Ep0001013 Ep0002014 Ep0010013 Ep0011013 "
    "Ep0020013 Ep0100011 Ep0101013 Ep0200013 Ep1000013 Ep1001013 Ep1010013 "
    "Ep1100013 Ep2000026 Eq0000013 Eq0001013 Eq0002013 Eq0010013 Eq0011013 "
    "Eq0100013 Eq0101013 Eq0110013 Eq1000013 Eq2000013 Er0000019 Er0001013 "
    "Er0010013 Er0011013 Er0020013 Er0101013 Er0200013 Er1000013 Er1001013 "
    "Er1010013 Er1100013 Es0000013 Es0001013 Es0002013 Es0010013 Es0011013 "
    "Es0100013 Es0101013 Es0110013 Es1000013 Es2000013 Et0000014 Et0001013 "
    "Et0010016 Et0011024 Et0020024 Et0101024 Et0200024 Et1000024 Et1001024 "
    "Et1010024 Et1100024 Eu0000024 Eu0001024 Eu0002024 Eu0010024 Eu0011024 "
    "Eu0020009 Eu0100024 Eu0101024 Eu0110024 Eu0200013 Eu1000024 Eu1001026 "
    "Eu1010005 Eu1100026 Eu2000024 Ev0000016 Ev0001024 Ev0002004 Ev0010024 "
    "Ev0011024 Ev0020024 Ev0101024 Ev0200024 Ev1000024 Ev1001024 Ev1010024 "
    "Ev1100024 Ew0000013 Ew0001013 Ew0002013 Ew0010013 Ew0011013 Ew0100013 "
    "Ew0101013 Ew0110013 Ew1000017 Ew2000017 Ex0000023 Ex0001017 Ex0002006 "
    "Ex0010017 Ex0011017 Ex0020017 Ex0100001 Ex0101017 Ex0200017 Ex1000017 "
    "Ex1001017 Ex1010017 Ex1100017 Ex2000025 "
)

CERT_L19_R0 = (
    "Sa0000051 Sa0001081 Sa0002174 Sa0003033 Sa0004199 Sa0010123 Sa0011027 "
    "Sa0012147 Sa0013149 Sa0020029 Sa0021144 Sa0030211 Sa0100239 Sa0101115 "
    "Sa0102069 Sa0103238 Sa0110074 Sa0111242 Sa0112108 Sa0120124 Sa0200157 "
    "Sa0201208 Sa0202039 Sa0210198 Sa0211213 Sa0300193 Sa1000164 Sa1001040 "
    "Sa1002052 Sa1003082 Sa1010204 Sa1011190 Sa1012131 Sa1100035 Sa1101099 "
    "Sa1200135 Sa2000150 Sb0000051 Sb0001216 Sb0002018 Sb0003149 Sb0004074 "
    "Sb0010177 Sb0011018 Sb0012123 Sb0013084 Sb0020011 Sb0021024 Sb0022027 "
    "Sb0030205 Sb0100158 Sb0101172 Sb0102128 Sb0103007 Sb0110011 Sb0111130 "
    "Sb0120099 Sb0200049 Sb0201196 Sb0202029 Sb0210121 Sb0211073 Sb0300226 "
    "Sb1000068 Sb1001019 Sb1002102 Sb1010081 Sb1011113 Sb1020018 Sb1100046 "
    "Sb1101128 Sb1200213 Sb2000018 Sc0000041 Sc0001049 Sc0002170 Sc0003016 "
    "Sc0004002 Sc0010051 Sc0012009 Sc0013145 Sc0020029 Sc0021021 Sc0022168 "
    "Sc0030099 Sc0100164 Sc0101175 Sc0102056 Sc0103071 Sc0110092 Sc0111013 "
    "Sc0112177 Sc0120213 Sc0200113 Sc0201094 Sc0202196 Sc0210196 Sc0211148 "
    "Sc0300112 Sc1000189 Sc1001085 Sc1002023 Sc1020072 Sc1100059 Sc1101092 "
    "Sc1200082 Sc2000101 Sd0000231 Sd0001237 Sd0002027 Sd0003092 Sd0010054 "
    "Sd0011033 Sd0012079 Sd0020218 Sd0021041 Sd0030130 Sd0100073 Sd0101116 "
    "Sd0102222 Sd0110021 Sd0111095 Sd0120153 Sd0200142 Sd0201189 Sd0210201 "
    "Sd0300183 Sd1000201 Sd1001054 Sd1010051 Sd1020170 Sd1100020 Sd1101015 "
    "Sd1200194 Sd2000241 Se0000145 Se0001117 Se0002233 Se0003089 Se0004053 "
    "Se0010190 Se0011072 Se0012049 Se0013051 Se0020071 Se0021007 Se0022231 "
    "Se0030148 Se0100024 Se0101148 Se0102143 Se0103042 Se0110059 Se0111077 "
    "Se0112096 Se0120238 Se0200038 Se0201026 Se0202129 Se0210235 Se0211103 "
    "Se0300142 Se1000049 Se1001242 Se1002074 Se1003090 Se1010091 Se1020141 "
    "Se1100224 Se1101110 Se1200052 Se2000202 Sf0000114 Sf0001076 Sf0002016 "
    "Sf0003080 Sf0010059 Sf0011192 Sf0012079 Sf0013075 Sf0020057 Sf0021007 "
    "Sf0030034 Sf0100215 Sf0101052 Sf0102216 Sf0110181 Sf0200005 Sf0201136 "
    "Sf0210075 Sf0300231 Sf1000153 Sf1001162 Sf1010170 Sf1020040 Sf1100131 "
    "Sf2000049 Sg0020077 Si0000231 Si0001071 Si0002049 Si0003075 Si0004088 "
    "Si0010146 Si0011120 Si0012181 Si0013037 Si0020077 Si0021135 Si0022099 "
    "Si0030166 Si0100045 Si0101074 Si0102085 Si0103129 Si0110103 Si0111109 "
    "Si0112004 Si0120020 Si0200200 Si0201086 Si0202080 Si0210082 Si0211196 "
    "Si0300026 Si1000058 Si1001033 Si1002013 Si1003009 Si1010111 Si1011008 "
    "Si1020146 Si1100242 Si1101106 Si1102209 Si1200141 Si2000120 Sj0000051 "
    "Sj0001096 Sj0002112 Sj0003115 Sj0004179 Sj0010024 Sj0011111 Sj0012145 "
    "Sj0013146 Sj0020083 Sj0021212 Sj0022012 Sj0030230 Sj0100062 Sj0101153 "
    "Sj0102200 Sj0103080 Sj0110016 Sj0111097 Sj0112082 Sj0120059 Sj0200057 "
    "Sj0201204 Sj0202070 Sj0210180 Sj0211097 Sj0300003 Sj1000201 Sj1001204 "
    "Sj1002137 Sj1010204 Sj1011122 Sj1020024 Sj1100029 Sj1101136 Sj1200129 "
    "Sj2000064 Sk0000234 Sk0001128 Sk0002004 Sk0003077 Sk0010013 Sk0011112 "
    "Sk0012156 Sk0013017 Sk0020037 Sk0021206 Sk0100039 Sk0101235 Sk0102183 "
    "Sk0103242 Sk0110119 Sk0111004 Sk0120165 Sk0200089 Sk0201205 Sk0202164 "
    "Sk0210201 Sk0300037 Sk1000094 Sk1001236 Sk1002060 Sk1010209 Sk1011203 "
    "Sk1020129 Sk1100173 Sk1101228 Sk1200063 Sk2000227 Sk2100162 Sl0000132 "
    "Sl0001225 Sl0002100 Sl0010180 Sl0011150 Sl0020233 Sl0021032 Sl0030113 "
    "Sl0100121 Sl0101143 Sl0102079 Sl0103145 Sl0110062 Sl0111080 Sl0120016 "
    "Sl0200082 Sl0201206 Sl0202070 Sl0210081 Sl0211057 Sl0300012 Sl1000107 "
    "Sl1001207 Sl1002103 Sl1010152 Sl1011154 Sl1020018 Sl1100140 Sl1101087 "
    "Sl1200024 Sl2000096 So0000162 So0100097 Sp0000213 Sp0001107 Sp0002239 "
    "Sp0004135 Sp0010235 Sp0011104 Sp0012225 Sp0013050 Sp0020125 Sp0021190 "
    "Sp0022130 Sp0030077 Sp0100171 Sp0101070 Sp0102025 Sp0103089 Sp0110125 "
    "Sp0111015 Sp0120079 Sp0200190 Sp0201103 Sp0202143 Sp0210241 Sp0211189 "
    "Sp0300225 Sp1000068 Sp1001092 Sp1010193 Sp1020223 Sp1100117 Sp1101103 "
    "Sp1110132 Sp1200083 Sp2000138 Sp2100151 Sr0000155 Sr0001180 Sr0002049 "
    "Sr0003043 Sr0100215 Sr0101138 Sr0102184 Sr0200070 Sr0201103 Sr1100242 "
    "St0000038 Su0100041 Ua0000192 Ua0001162 Ua0002150 Ua0003148 Ua0010039 "
    "Ua0011225 Ua0012159 Ua0020205 Ua0030226 Ua0100058 Ua0101236 Ua0102006 "
    "Ua0110055 Ua0120052 Ua0200196 Ua0201218 Ua0210015 Ua0300107 Ua1001203 "
    "Ua1020003 Ua1101020 Ua1200165 Ub0000101 Ub0001108 Ub0002183 Ub0010116 "
    "Ub0011198 Ub0020091 Ub0021170 Ub0030089 Ub0100234 Ub0101065 Ub0102070 "
    "Ub0110124 Ub0200176 Ub0201182 Ub0300005 Ub1000205 Ub1001224 Ub1010009 "
    "Ub1011072 Ub1100181 Ub1200180 Ub2000225 Uc0000075 Uc0001090 Uc0002109 "
    "Uc0003141 Uc0004146 Uc0010174 Uc0011117 Uc0012093 Uc0013037 Uc0020241 "
    "Uc0021114 Uc0030192 Uc0100093 Uc0101039 Uc0102207 Uc0103138 Uc0110130 "
    "Uc0111203 Uc0120091 Uc0200221 Uc0201130 Uc0202070 Uc0210074 Uc0211198 "
    "Uc0300002 Uc1000004 Uc1001227 Uc1002116 Uc1010045 Uc1011041 Uc1020069 "
    "Uc1100184 Uc1101020 Uc1200221 Uc2000126 Ud0000020 Ud0001060 Ud0011224 "
    "Ud0030068 Ud0200182 Ud1000169 Ue0000133 Ue0001056 Ue0002124 Ue0011181 "
    "Ue0100176 Ue0101050 Ue0200225 Ue0201223 Uf0000139 Uf0001206 Ug1010131 "
    "Ug1020202 Ug1200085 Ug2000214 Ug2002108 Ug4000027 Uh0102230 Ui0004137 "
    "Ui0012201 Ui0100079 Ui0110212 Ui0120209 Ui0200063 Ui0201130 Ui0300098 "
    "Ui1002092 Ui1010116 Ui1100028 Ui1101131 Ui1111236 Uj0030098 Uj4000025 "
    "Uk0000007 Uk0021001 Uk0022153 Uk0100154 Uk0110229 Uk0111087 Uk0112075 "
    "Uk0200210 Uk0201231 Uk0211089 Uk1011240 Uk2011077 Ul0012191 Ul3010242 "
    "Um0010112 Um0011108 Um0020007 Um0021168 Um0100140 Um0101065 Um0102220 "
    "Um0111014 Um0112236 Um0130237 Um0200115 Um0202129 Um0211031 Um1000054 "
    "Um1001171 Um1010185 Um1020172 Um2000182 Un0002141 Uo0000091 Uo0004210 "
    "Uo0010220 Uo0012099 Uo0020015 Uo0021022 Uo0022200 Uo0100004 Uo0110057 "
    "Uo0120073 Uo1111142 Uo3010044 Uo4000018 Up1020040 Up2000147 Up2002004 "
    "Up3000239 Up3001168 Up4000213 Uq0000015 Uq0002146 Uq0004165 Uq0010230 "
    "Uq0011206 Uq0012160 Uq0021219 Uq0022070 Uq0100130 Uq0102028 Uq0110212 "
    "Uq0200140 Uq0201228 Uq0211068 Uq1100196 Uq1102137 Uq1111023 Uq2101017 "
    "Ur0020148 Ur0100174 Ur2100015 Ur3010240 Us0001118 Us0010151 Us0011095 "
    "Us0020121 Us0030041 Us1010109 Ut1100097 Ut1102038 Ut2000238 Ut2001019 "
    "Ut2011213 Ut2101067 Ut3001086 Uu0000123 Uu0001028 Uu0004019 Uu0010017 "
    "Uu0012142 Uu0020042 Uu0100071 Uu0101032 Uu0110025 Uu0120110 Uu1000190 "
    "Uu1010011 Uu4000121 Uw0000192 Uw0002122 Uw0004124 Uw0021186 Uw0100136 "
    "Uw0102228 Uw0211097 Uw1102031 Uw1111173 Ux0100031 Ux0120215 Ux1000153 "
    "Ux1002221 Ux1100093 Ux1101203 Ux1111167 Ux2000016 Ux2001165 Ux2100043 "
    "Ux3000221 Ux3010024 Ux4000023 Ea0020063 Eb0102199 Eb1011033 Eb1100235 "
    "Eb1200144 Eb2000207 Eb2001086 Ec0000088 Ec0001166 Ec0010153 Ec0012216 "
    "Ec0110017 Ec1002214 Ec1010201 Ed0030215 Ed0200007 Ed1000097 Ed1001072 "
    "Ed1010162 Ed1020138 Ed1100162 Ed1101182 Ed1200109 Ed3000111 Ee0000001 "
    "Ee0002190 Ee0100082 Ee0102118 Ee0110070 Ef1000096 Ef1010156 Eh0100009 "
    "Ei0010087 Ei1010201 Ei3010065 Ej0020021 Ej0021150 Ej0030199 Ej0111076 "
    "Ej0112060 Ej0200020 Ej0202197 Ej0211091 Ej0300086 Ej1000114 Ej1001016 "
    "Ej1010225 Ej1011162 Ej1020069 Ej1200042 Ej2000214 Ej4000009 Ek0002092 "
    "Ek0004139 Ek0102038 Ek0110148 Ek2101078 El0010078 El0012102 El0100078 "
    "El0101174 El0110073 El0111094 El0120153 El0200158 El0201076 El0202143 "
    "El0300238 El1000067 El1002017 El1010007 El1100101 El1101125 El1111078 "
    "El3000236 Em0030119 Em0211094 Em4000012 En0000117 En0002029 En0021072 "
    "En0022100 En0100034 En0102118 En0110114 En0111127 En0112131 En0120014 "
    "En0200089 En0201115 En1011134 En1100064 En1102026 En2011201 Eo0012155 "
    "Eo0020096 Eo3000063 Eo3010062 Ep0010158 Ep0011127 Ep0020015 Ep0021066 "
    "Ep0030077 Ep0100230 Ep0101030 Ep0102145 Ep0111057 Ep0112016 Ep0200220 "
    "Ep0202198 Ep0211037 Ep1000233 Ep1001061 Ep1010189 Ep1011117 Ep1020146 "
    "Ep2000110 Ep2002074 Ep2011020 Eq0002164 Eq0004100 Eq0110163 Eq2101071 "
    "Er0000139 Er0001012 Er0010124 Er0012036 Er0100160 Er0101239 Er0110128 "
    "Er0111078 Er0120159 Er0300073 Er1000157 Er1002010 Es1020177 Et0000215 "
    "Et0010153 Et0100229 Et0200016 Et0201177 Et1100147 Eu0020156 Eu1002054 "
    "Eu1111011 Eu2100051 Eu3000092 Eu3010079 Eu4000201 Ev0000091 Ev0001242 "
    "Ev0002011 Ev0010190 Ev0011231 Ev0020220 Ev0021186 Ev0030168 Ev0111129 "
    "Ev0112133 Ev0200035 Ev0202189 Ev1010112 Ev1011066 Ev1020212 Ev2002135 "
    "Ev2011086 Ew0001006 Ew0002006 Ew0003006 Ew0010006 Ew0011006 Ew0012006 "
    "Ew0013006 Ew0020006 Ew0021006 Ew0022006 Ew0030006 Ew0031006 Ew0040006 "
    "Ew0100006 Ew0101006 Ew0102006 Ew0103006 Ew0110006 Ew0111006 Ew0112006 "
    "Ew0120006 Ew0121006 Ew0130006 Ew0200006 Ew0201006 Ew0202006 Ew0210006 "
    "Ew0211006 Ew0220006 Ew0300006 Ew0310006 Ew0400006 Ew1000006 Ew1001006 "
    "Ew1002006 Ew1003006 Ew1010006 Ew1011006 Ew1012006 Ew1020006 Ew1021006 "
    "Ew1100173 Ew1101006 Ew1110006 Ew1111006 Ew1120006 Ew1200006 Ew1201006 "
    "Ew1210006 Ew1300006 Ew2000101 Ew2002006 Ew2010006 Ew2100006 Ew2110006 "
    "Ew3100006 Ew4000006 Ex0000165 Ex0001114 Ex0002006 Ex0003006 Ex0010127 "
    "Ex0011006 Ex0012126 Ex0013006 Ex0020142 Ex0021006 Ex0022006 Ex0030006 "
    "Ex0031006 Ex0040006 Ex0100083 Ex0101209 Ex0102006 Ex0103006 Ex0110132 "
    "Ex0111124 Ex0112006 Ex0121006 Ex0130006 Ex0200006 Ex0201006 Ex0202006 "
    "Ex0210006 Ex0211006 Ex0220006 Ex0300006 Ex0301006 Ex0310006 Ex1000219 "
    "Ex1001006 Ex1002193 Ex1003006 Ex1010078 Ex1011006 Ex1012006 Ex1020006 "
    "Ex1021006 Ex1030006 Ex1100006 Ex1101006 Ex1102006 Ex1110006 Ex1111006 "
    "Ex1120006 Ex1200006 Ex1210006 Ex2000006 Ex2001006 Ex2002006 Ex2010006 "
    "Ex2011006 Ex2020006 Ex2100006 Ex2101006 Ex2110006 Ex2200006 Ex3000006 "
    "Ex3001006 Ex3010006 Ex3100006 Ex4000083 "
)

CERT_L19_R1 = (
    "Sa0000162 Sa0001105 Sa0002117 Sa0003192 Sa0004177 Sa0010165 Sa0011168 "
    "Sa0012182 Sa0013137 Sa0020230 Sa0021048 Sa0022176 Sa0030221 Sa0100104 "
    "Sa0101076 Sa0102176 Sa0103083 Sa0110041 Sa0111224 Sa0120013 Sa0121239 "
    "Sa0200028 Sa0201170 Sa0202156 Sa0210179 Sa0300188 Sa1000235 Sa1001182 "
    "Sa1002086 Sa1003112 Sa1010189 Sa1011059 Sa1012055 Sa1100146 Sa1101212 "
    "Sa1200093 Sa2000051 Sb0000054 Sb0001042 Sb0002078 Sb0003168 Sb0004178 "
    "Sb0010165 Sb0011078 Sb0012188 Sb0013166 Sb0020050 Sb0021177 Sb0022030 "
    "Sb0030167 Sb0100104 Sb0101112 Sb0102079 Sb0103089 Sb0110224 Sb0111016 "
    "Sb0120060 Sb0200015 Sb0201117 Sb0202227 Sb0210128 Sb0300191 Sb1000070 "
    "Sb1001014 Sb1002030 Sb1010024 Sb1011177 Sb1020240 Sb1100015 Sb1101221 "
    "Sb1200010 Sb2000144 Sc0000138 Sc0001219 Sc0002045 Sc0003042 Sc0004191 "
    "Sc0010147 Sc0011159 Sc0012047 Sc0013216 Sc0020122 Sc0021069 Sc0022060 "
    "Sc0030213 Sc0100138 Sc0101132 Sc0102068 Sc0103176 Sc0110110 Sc0111080 "
    "Sc0120121 Sc0200223 Sc0201238 Sc0202167 Sc0210174 Sc0300068 Sc1000180 "
    "Sc1001125 Sc1002222 Sc1020228 Sc1100108 Sc1101121 Sc1102123 Sc1110152 "
    "Sc1200139 Sc2000238 Sd0000210 Sd0001180 Sd0002021 Sd0003046 Sd0010111 "
    "Sd0011132 Sd0012061 Sd0020218 Sd0021029 Sd0030109 Sd0100073 Sd0101068 "
    "Sd0102076 Sd0110237 Sd0111117 Sd0120114 Sd0200234 Sd0201222 Sd0210106 "
    "Sd0300188 Sd1000156 Sd1001164 Sd1010171 Sd1020006 Sd1100214 Sd1101172 "
    "Sd1200028 Sd2000143 Se0000156 Se0001166 Se0002050 Se0003140 Se0004101 "
    "Se0010139 Se0011027 Se0012208 Se0013046 Se0020098 Se0021010 Se0022235 "
    "Se0030118 Se0100041 Se0101035 Se0102015 Se0103025 Se0110206 Se0111191 "
    "Se0120030 Se0200171 Se0201045 Se0202038 Se0210134 Se0300177 Se1000130 "
    "Se1001191 Se1002090 Se1003139 Se1010226 Se1011127 Se1020094 Se1100106 "
    "Se1101228 Se1200152 Se2000200 Sf0000134 Sf0001188 Sf0002067 Sf0003171 "
    "Sf0010116 Sf0011093 Sf0012232 Sf0020003 Sf0021007 Sf0022234 Sf0030076 "
    "Sf0100035 Sf0101016 Sf0102072 Sf0103063 Sf0110010 Sf0200062 Sf0201178 "
    "Sf0300177 Sf1000048 Sf1001219 Sf1010113 Sf1020118 Sf1100157 Sf2000047 "
    "Sg0020095 Si0000183 Si0001176 Si0002184 Si0003120 Si0004101 Si0010215 "
    "Si0011240 Si0012224 Si0013135 Si0020095 Si0021183 Si0022195 Si0030190 "
    "Si0100018 Si0101122 Si0102002 Si0103199 Si0110117 Si0111161 Si0120040 "
    "Si0200164 Si0201109 Si0202174 Si0210164 Si0300038 Si1000190 Si1001231 "
    "Si1002145 Si1003171 Si1010183 Si1011003 Si1012201 Si1020056 Si1100152 "
    "Si1101238 Si1200010 Si2000117 Sj0000216 Sj0001123 Sj0002043 Sj0003229 "
    "Sj0004193 Sj0010192 Sj0011177 Sj0012012 Sj0013131 Sj0020098 Sj0021080 "
    "Sj0022006 Sj0030107 Sj0100224 Sj0101153 Sj0102026 Sj0103190 Sj0110121 "
    "Sj0111035 Sj0120098 Sj0200201 Sj0201171 Sj0202114 Sj0210082 Sj0300237 "
    "Sj1000216 Sj1001237 Sj1002120 Sj1010147 Sj1011149 Sj1020012 Sj1100153 "
    "Sj1101071 Sj1200186 Sj2000085 Sk0000213 Sk0001185 Sk0002109 Sk0003092 "
    "Sk0010136 Sk0011100 Sk0012211 Sk0020106 Sk0021050 Sk0100025 Sk0101120 "
    "Sk0102066 Sk0103079 Sk0110046 Sk0111033 Sk0120144 Sk0200093 Sk0201185 "
    "Sk0202176 Sk0300049 Sk1000190 Sk1001238 Sk1002039 Sk1010047 Sk1011033 "
    "Sk1020220 Sk1100188 Sk1101119 Sk1110171 Sk1200207 Sk2000033 Sk2100019 "
    "Sl0000072 Sl0001078 Sl0002139 Sl0003099 Sl0010051 Sl0011036 Sl0020125 "
    "Sl0021086 Sl0022063 Sl0030059 Sl0100237 Sl0101055 Sl0102006 Sl0103188 "
    "Sl0110201 Sl0111100 Sl0120114 Sl0200087 Sl0201225 Sl0210220 Sl0300176 "
    "Sl1000001 Sl1001237 Sl1010088 Sl1011016 Sl1020114 Sl1100143 Sl1101209 "
    "Sl1200117 Sl2000045 So0000063 So0100074 Sp0000163 Sp0001211 Sp0002058 "
    "Sp0003115 Sp0004210 Sp0010125 Sp0011079 Sp0012065 Sp0013175 Sp0020058 "
    "Sp0021131 Sp0030096 Sp0100012 Sp0101039 Sp0102188 Sp0103037 Sp0110189 "
    "Sp0111036 Sp0120230 Sp0200220 Sp0201110 Sp0202050 Sp0210038 Sp0300213 "
    "Sp1000188 Sp1001146 Sp1002156 Sp1010239 Sp1020054 Sp1100126 Sp1101036 "
    "Sp1200189 Sp2000063 Sp2100035 Sr0000115 Sr0001051 Sr0002097 Sr0003120 "
    "Sr0100053 Sr0101200 Sr0200017 Sr0201027 Sr1100166 St0000178 Su0100211 "
    "Ua0000108 Ua0001039 Ua0002039 Ua0010159 Ua0011111 Ua0012082 Ua0020220 "
    "Ua0030239 Ua0100157 Ua0101062 Ua0110085 Ua0200014 Ua0201061 Ua0210211 "
    "Ua0300220 Ua1001037 Ua1020001 Ua1101116 Ua1200215 Ub0000049 Ub0001228 "
    "Ub0002174 Ub0010045 Ub0011030 Ub0020142 Ub0030136 Ub0100209 Ub0101074 "
    "Ub0102149 Ub0110107 Ub0200075 Ub0201240 Ub0210099 Ub0300103 Ub1000107 "
    "Ub1001175 Ub1010057 Ub1011108 Ub1100154 Ub1101086 Ub1200099 Ub2000114 "
    "Uc0000005 Uc0001082 Uc0002233 Uc0003209 Uc0004029 Uc0010159 Uc0011183 "
    "Uc0012130 Uc0013053 Uc0020076 Uc0021042 Uc0030132 Uc0100175 Uc0101155 "
    "Uc0102178 Uc0103143 Uc0110139 Uc0111127 Uc0120078 Uc0200241 Uc0201138 "
    "Uc0202189 Uc0210031 Uc0300100 Uc1000002 Uc1001169 Uc1002152 Uc1010162 "
    "Uc1011053 Uc1020162 Uc1100093 Uc1200056 Uc2000135 Ud0000203 Ud0001099 "
    "Ud0011205 Ud0030210 Ud0100135 Ud0200009 Ud1000196 Ue0000128 Ue0001150 "
    "Ue0011001 Ue0100139 Ue0101013 Ue0200140 Ue2011188 Uf0000065 Uf0001028 "
    "Ug0202074 Ug1010174 Ug1120019 Ug1200099 Ug2000098 Ug2002091 Ug4000001 "
    "Uh0102056 Uh0110007 Ui0110059 Ui0120014 Ui0200086 Ui0201010 Ui0300048 "
    "Ui1000012 Ui1002060 Ui1010022 Ui1100127 Ui1101194 Ui2200032 Ui3000217 "
    "Uj0030142 Uj4000072 Uk0000085 Uk0002216 Uk0021004 Uk0022006 Uk0110116 "
    "Uk0111086 Uk0200140 Uk0201093 Uk1011165 Uk2011144 Ul0012024 Ul2200136 "
    "Ul3010020 Um0010046 Um0011013 Um0020142 Um0021033 Um0100120 Um0101014 "
    "Um0102081 Um0111236 Um0200033 Um0202118 Um1000185 Um1001016 Um1010234 "
    "Um1011161 Um1020115 Um2000032 Un0002206 Un0110045 Un2101223 Uo0000059 "
    "Uo0001162 Uo0004206 Uo0010195 Uo0012181 Uo0020213 Uo0021153 Uo0022110 "
    "Uo0100128 Uo0110085 Uo0111204 Uo0120084 Uo3010180 Uo4000062 Up1020028 "
    "Up2000083 Up2002077 Up3000162 Up3001228 Up4000166 Uq0000201 Uq0002038 "
    "Uq0004222 Uq0010056 Uq0011128 Uq0012040 Uq0021078 Uq0022026 Uq0040075 "
    "Uq0100017 Uq0102164 Uq0110102 Uq0200021 Uq0201232 Uq1100237 Uq1102226 "
    "Uq2101042 Uq2200083 Ur0020157 Ur2200064 Ur3000063 Ur3010031 Us0001022 "
    "Us0010238 Us0011182 Us0020139 Us0030005 Us0111176 Us1010151 Ut1100084 "
    "Ut1102154 Ut2000230 Ut2001217 Ut2011099 Ut2101136 Ut3000185 Ut3001146 "
    "Uu0000203 Uu0001041 Uu0004068 Uu0010239 Uu0012076 Uu0020141 Uu0100114 "
    "Uu0101013 Uu0110181 Uu0111019 Uu0120142 Uu1000212 Uu1010172 Uu1201204 "
    "Uv0202184 Uv2100013 Uw0002032 Uw0004123 Uw0021192 Uw0022086 Uw0100103 "
    "Uw0102052 Uw1102125 Uw2200187 Ux0100046 Ux0120033 Ux1000156 Ux1002225 "
    "Ux1100020 Ux1120185 Ux1201137 Ux2000205 Ux2001182 Ux2100166 Ux2200049 "
    "Ux3000137 Ux3010039 Ux4000102 Eb0102073 Eb1100026 Eb1200155 Eb2000123 "
    "Ec0000106 Ec0001024 Ec0010018 Ec0012201 Ec0110231 Ec1010120 Ed0030217 "
    "Ed0200138 Ed1000188 Ed1001153 Ed1010111 Ed1020134 Ed1100052 Ed1101096 "
    "Ed1200109 Ee0000059 Ee0002079 Ee0100029 Ee0102094 Ee0110225 Ef1000012 "
    "Ef1010099 Eg0020036 Eh0100144 Eh0200002 Ei0010054 Ei1010057 Ei3010128 "
    "Ej0020198 Ej0021168 Ej0030046 Ej0111102 Ej0200037 Ej0202144 Ej0300120 "
    "Ej1000216 Ej1001218 Ej1010108 Ej1011088 Ej1020080 Ej1200142 Ej2000168 "
    "Ej2002019 Ej4000026 Ek0002122 Ek0004237 Ek0102116 Ek0110178 Ek2101132 "
    "El0004076 El0010129 El0012155 El0100123 El0101201 El0110215 El0111237 "
    "El0120070 El0200213 El0300156 El1000020 El1002016 El1010095 El1100041 "
    "El1101110 El1120157 El2200152 El3000130 El4000143 Em0030100 Em2002089 "
    "Em4000225 En0000022 En0002199 En0021216 En0022041 En0100059 En0102008 "
    "En0110009 En0111098 En0120209 En0200186 En0201218 En1011206 En1100123 "
    "En1102177 En2011087 En2200225 Eo0012241 Eo0020036 Eo2200094 Eo3000096 "
    "Eo3010134 Ep0010175 Ep0011032 Ep0020133 Ep0021116 Ep0030066 Ep0100002 "
    "Ep0101013 Ep0102087 Ep0111201 Ep0200138 Ep0202039 Ep1000160 Ep1001158 "
    "Ep1010096 Ep1011076 Ep1020050 Ep2000013 Ep2002027 Ep2011114 Eq0002008 "
    "Eq0004112 Eq0110032 Eq2101211 Er0000020 Er0001210 Er0010080 Er0012228 "
    "Er0100031 Er0101167 Er0110097 Er0120174 Er0300217 Er1000020 Er1002135 "
    "Es1020017 Et0000143 Et0010153 Et0100164 Et0200198 Et0201214 Eu0020117 "
    "Eu1002162 Eu1120002 Eu1201239 Eu2100225 Eu2200141 Eu3000083 Eu3010123 "
    "Eu4000046 Ev0000015 Ev0001129 Ev0002033 Ev0010204 Ev0011082 Ev0020056 "
    "Ev0021011 Ev0030050 Ev0111234 Ev0200197 Ev0202110 Ev1010038 Ev1011104 "
    "Ev1020125 Ev2002048 Ev2011066 Ew0001168 Ew0002168 Ew0003168 Ew0004011 "
    "Ew0010168 Ew0011168 Ew0012168 Ew0013168 Ew0020168 Ew0021168 Ew0022168 "
    "Ew0030168 Ew0031168 Ew0040168 Ew0100168 Ew0101168 Ew0102168 Ew0103168 "
    "Ew0110168 Ew0111168 Ew0112168 Ew0120168 Ew0121168 Ew0130168 Ew0200168 "
    "Ew0201168 Ew0202168 Ew0210168 Ew0211168 Ew0220168 Ew0300168 Ew0310168 "
    "Ew0400168 Ew1000168 Ew1001168 Ew1002168 Ew1003168 Ew1010168 Ew1011168 "
    "Ew1012168 Ew1020168 Ew1021168 Ew1100178 Ew1101168 Ew1110168 Ew1111168 "
    "Ew1120168 Ew1200168 Ew1201168 Ew1210168 Ew1300168 Ew2000158 Ew2002168 "
    "Ew2010168 Ew2100168 Ew2110168 Ew3000113 Ew3100168 Ew4000168 Ex0001027 "
    "Ex0002168 Ex0003168 Ex0004033 Ex0010010 Ex0011168 Ex0012017 Ex0013168 "
    "Ex0020112 Ex0021168 Ex0022168 Ex0030168 Ex0031168 Ex0040168 Ex0100206 "
    "Ex0101066 Ex0102168 Ex0103168 Ex0110032 Ex0111034 Ex0112168 Ex0120192 "
    "Ex0121168 Ex0130168 Ex0200168 Ex0201168 Ex0202168 Ex0210168 Ex0211168 "
    "Ex0220168 Ex0300168 Ex0301168 Ex0310168 Ex1000114 Ex1001168 Ex1002190 "
    "Ex1003168 Ex1010184 Ex1011168 Ex1012168 Ex1020168 Ex1021168 Ex1030168 "
    "Ex1100168 Ex1101168 Ex1102168 Ex1110168 Ex1111168 Ex1120168 Ex1200168 "
    "Ex1201030 Ex1210168 Ex2000168 Ex2001168 Ex2002168 Ex2010168 Ex2011168 "
    "Ex2020168 Ex2100168 Ex2101168 Ex2110168 Ex2200168 Ex3000168 Ex3001168 "
    "Ex3010168 Ex3100168 Ex4000215 "
)

CERT_L19_R2 = (
    "Sa0000044 Sa0001044 Sa0002077 Sa0003057 Sa0010063 Sa0011006 Sa0012028 "
    "Sa0020026 Sa0100041 Sa0101061 Sa0102066 Sa0110019 Sa0111070 Sa0200023 "
    "Sa1000021 Sa1001047 Sa1010032 Sa1100042 Sb0000018 Sb0001018 Sb0002035 "
    "Sb0003059 Sb0010046 Sb0011028 Sb0012034 Sb0020056 Sb0100056 Sb0101038 "
    "Sb0102043 Sb0110009 Sb0200070 Sb0201076 Sb1000046 Sb1001078 Sb1100065 "
    "Sc0000059 Sc0001077 Sc0002020 Sc0003053 Sc0010065 Sc0011016 Sc0012035 "
    "Sc0020062 Sc0100001 Sc0101046 Sc0102055 Sc0110063 Sc0120067 Sc0200002 "
    "Sc0210003 Sc1000015 Sc1001063 Sc1010008 Sc1100048 Sd0000061 Sd0001025 "
    "Sd0002028 Sd0003034 Sd0010051 Sd0011002 Sd0012035 Sd0020044 Sd0100056 "
    "Sd0101041 Sd0110018 Sd0200017 Sd1000056 Sd1001035 Sd1010058 Sd1100073 "
    "Se0000019 Se0001069 Se0002073 Se0003002 Se0010019 Se0011078 Se0012012 "
    "Se0020075 Se0100078 Se0101066 Se0102030 Se0110017 Se0120070 Se0200037 "
    "Se0201004 Se1000060 Se1001023 Se1010037 Se1100020 Se2000079 Sf0000060 "
    "Sf0001024 Sf0010068 Sf0011050 Sf0020007 Sf0100065 Sf0101010 Sf0110079 "
    "Sf0200068 Sf0210064 Sf1000006 Sf1100007 Sg0100067 Sh0100044 Si0000063 "
    "Si0001061 Si0002075 Si0003072 Si0010028 Si0011068 Si0012054 Si0020052 "
    "Si0100012 Si0102058 Si0110046 Si0111073 Si0200022 Si1000059 Si1001047 "
    "Si1010036 Si1100075 Sj0000034 Sj0001058 Sj0002027 Sj0010062 Sj0011002 "
    "Sj0012045 Sj0020009 Sj0100038 Sj0101004 Sj0102049 Sj0110019 Sj0200011 "
    "Sj1000018 Sj1001020 Sj1010048 Sj1100053 Sk0000073 Sk0001026 Sk0002058 "
    "Sk0010045 Sk0011077 Sk0020078 Sk0101063 Sk0110028 Sk0200012 Sk1000042 "
    "Sk1001010 Sk1010053 Sk1100047 Sl0000017 Sl0001023 Sl0002001 Sl0010048 "
    "Sl0011005 Sl0020040 Sl0100038 Sl0101037 Sl0110049 Sl0200056 Sl1000023 "
    "Sl1010051 Sl1100032 Sm0000042 Sn0100034 Sp0000028 Sp0001030 Sp0002022 "
    "Sp0003038 Sp0010053 Sp0011025 Sp0020010 Sp0100007 Sp0101011 Sp0110024 "
    "Sp0200059 Sp0210079 Sp1000033 Sp1010066 Sp1100009 Sq0100059 Sr0000066 "
    "Sr0001022 Sr0010068 Sr0011072 Sr0020030 Sr0100074 Sr0101016 Sr0110037 "
    "Sr0200010 Sr0210050 Su0100075 Sw0100042 Sx0000028 Ua0000077 Ua0010069 "
    "Ua0011009 Ua0020045 Ua0100065 Ua0101042 Ua0110006 Ua0200006 Ua1000047 "
    "Ua1100060 Ub0000044 Ub0001006 Ub0002042 Ub0010062 Ub0011040 Ub0020027 "
    "Ub0100046 Ub0101035 Ub0110051 Ub0200045 Ub1000011 Ub1010042 Ub1100053 "
    "Uc0000041 Uc0001058 Uc0002074 Uc0010059 Uc0011023 Uc0012060 Uc0020018 "
    "Uc0100023 Uc0101040 Uc0102061 Uc0110074 Uc0200006 Uc0201008 Uc1000043 "
    "Uc1010023 Uc1100019 Ud0000002 Ud0001034 Ud0010032 Ud0011074 Ud0020008 "
    "Ud0100031 Ud0101025 Ud0102033 Ud0200035 Ud1000054 Ud1010007 Ud1100037 "
    "Ue0000050 Ue0001072 Ue0010031 Ue0011043 Ue0020046 Ue0100018 Ue0101040 "
    "Ue0200064 Ue1010063 Ue1100032 Uf0000019 Uf0001042 Uf0010024 Uf0011077 "
    "Uf0020002 Uf0100003 Uf0101013 Uf0102071 Uf0200068 Ug0201044 Ug1020006 "
    "Ug2000051 Uh0000076 Uh0002076 Uh0100032 Ui1101028 Ui2000045 Uj0002059 "
    "Uj0100048 Uj0102067 Uj1002050 Uk1101025 Uk2000074 Ul0000072 Ul0002069 "
    "Ul0030063 Ul0100050 Ul0102018 Ul1002026 Um1101008 Um2000001 Un0000073 "
    "Un0002074 Un0010007 Uo1101019 Uo2000034 Uo2001069 Uo3000037 Up0000027 "
    "Up0002065 Up0010073 Up0100024 Up0102071 Up1002075 Up3000063 Uq1101053 "
    "Uq2000079 Uq3000077 Ur0000076 Ur0002067 Ur0010029 Ur0100074 Us2000062 "
    "Ut0000051 Ut0002058 Ut0010058 Ut0102073 Uu1101017 Uu2000042 Uu3000066 "
    "Uw1101079 Uw2000048 Uw3000063 Ux0000057 Ux0002044 Ux0010057 Ux0100006 "
    "Ux0102070 Ux0200068 Ux0201068 Ux0210068 Ux0300068 Ux1000033 Ux1001033 "
    "Ux1010044 Ux1011044 Ux1020044 Ux1100044 Ux1101044 Ux1110044 Ux1200044 "
    "Ux2000044 Ux2001044 Ux2010044 Ux2100044 Ea0000044 Ea0001044 Ea0002044 "
    "Ea0003044 Ea0010044 Ea0011044 Ea0012044 Ea0020044 Ea0021044 Ea0030044 "
    "Ea0100044 Ea0101044 Ea0102044 Ea0110044 Ea0111044 Ea0120044 Ea0200044 "
    "Ea0210044 Ea0300044 Ea1000044 Ea1001044 Ea1002044 Ea1010044 Ea1100044 "
    "Ea1110044 Ea1200044 Ea2010044 Ea2100044 Eb0000068 Eb0001044 Eb0002021 "
    "Eb0003044 Eb0010059 Eb0011044 Eb0012044 Eb0020044 Eb0021044 Eb0100042 "
    "Eb0101044 Eb0110044 Eb0111044 Eb0120044 Eb0200044 Eb0201044 Eb0210044 "
    "Eb0300044 Eb1000044 Eb1001044 Eb1010044 Eb1011044 Eb1020044 Eb1100044 "
    "Eb1101044 Eb1110044 Eb1200044 Eb2000044 Eb2001044 Eb2010044 Eb2100044 "
    "Ec0000044 Ec0001044 Ec0002044 Ec0003044 Ec0010044 Ec0011044 Ec0012044 "
    "Ec0020044 Ec0021044 Ec0030044 Ec0100044 Ec0101044 Ec0102044 Ec0110044 "
    "Ec0111044 Ec0120044 Ec0200044 Ec0201030 Ec0210044 Ec0300044 Ec1000044 "
    "Ec1001044 Ec1002044 Ec1010044 Ec1100044 Ec1110044 Ec1200044 Ec2000080 "
    "Ec2010044 Ec2100044 Ed0000027 Ed0001044 Ed0002050 Ed0003044 Ed0010021 "
    "Ed0011044 Ed0012044 Ed0020044 Ed0021044 Ed0100004 Ed0101044 Ed0102013 "
    "Ed0110044 Ed0111044 Ed0120044 Ed0200044 Ed0201044 Ed0210044 Ed0300044 "
    "Ed1000044 Ed1001044 Ed1010044 Ed1011044 Ed1020044 Ed1100044 Ed1101044 "
    "Ed1110044 Ed1200044 Ed2000044 Ed2001044 Ed2010044 Ed2100044 Ee0000044 "
    "Ee0001044 Ee0002044 Ee0003044 Ee0010044 Ee0011044 Ee0012044 Ee0020044 "
    "Ee0021044 Ee0030044 Ee0100044 Ee0101044 Ee0102044 Ee0110044 Ee0111044 "
    "Ee0120044 Ee0200044 Ee0210044 Ee0300044 Ee1000044 Ee1001044 Ee1002044 "
    "Ee1010044 Ee1100044 Ee1110044 Ee1200044 Ee2010044 Ee2100044 Ef0000019 "
    "Ef0001044 Ef0003044 Ef0010076 Ef0011044 Ef0012044 Ef0020044 Ef0021044 "
    "Ef0100076 Ef0101044 Ef0110044 Ef0111044 Ef0120044 Ef0200044 Ef0201044 "
    "Ef0210044 Ef0300044 Ef1000044 Ef1001044 Ef1010044 Ef1011044 Ef1020044 "
    "Ef1100044 Ef1101044 Ef1110044 Ef1200044 Ef2000044 Ef2001044 Ef2010044 "
    "Ef2100044 Eg0000044 Eg0001044 Eg0002044 Eg0003044 Eg0010044 Eg0011044 "
    "Eg0012044 Eg0020044 Eg0021044 Eg0030044 Eg0100044 Eg0101044 Eg0102044 "
    "Eg0110044 Eg0111044 Eg0120044 Eg0200044 Eg0210044 Eg0300044 Eg1000044 "
    "Eg1001044 Eg1002044 Eg1010044 Eg1100044 Eg1110044 Eg1200044 Eg2010044 "
    "Eg2100044 Eh0000035 Eh0001044 Eh0003044 Eh0010044 Eh0011044 Eh0012044 "
    "Eh0020044 Eh0021044 Eh0100024 Eh0101044 Eh0110044 Eh0111044 Eh0120044 "
    "Eh0200044 Eh0201044 Eh0210044 Eh0300044 Eh1000044 Eh1001044 Eh1010044 "
    "Eh1011044 Eh1020044 Eh1100044 Eh1101044 Eh1110044 Eh1200044 Eh2000044 "
    "Eh2001044 Eh2010044 Eh2100044 Ei0000044 Ei0001044 Ei0002044 Ei0003044 "
    "Ei0010044 Ei0011044 Ei0012044 Ei0020044 Ei0021044 Ei0030044 Ei0100044 "
    "Ei0101044 Ei0102044 Ei0110044 Ei0111044 Ei0120044 Ei0200044 Ei0201058 "
    "Ei0210044 Ei0300044 Ei1000044 Ei1001044 Ei1002044 Ei1010044 Ei1100044 "
    "Ei1110044 Ei1200044 Ei2000070 Ei2001048 Ei2010044 Ei2100044 Ei3000033 "
    "Ej0000073 Ej0001044 Ej0002060 Ej0003044 Ej0010047 Ej0011044 Ej0012044 "
    "Ej0020044 Ej0021044 Ej0100072 Ej0101044 Ej0102062 Ej0110044 Ej0111044 "
    "Ej0120044 Ej0200044 Ej0201044 Ej0210044 Ej0300044 Ej1000044 Ej1001044 "
    "Ej1002009 Ej1010044 Ej1011044 Ej1020044 Ej1100044 Ej1101044 Ej1110044 "
    "Ej1200044 Ej2000044 Ej2001044 Ej2010044 Ej2100044 Ek0000044 Ek0001044 "
    "Ek0002044 Ek0003044 Ek0010044 Ek0011044 Ek0012044 Ek0020044 Ek0021044 "
    "Ek0030044 Ek0100044 Ek0101044 Ek0102044 Ek0110044 Ek0111044 Ek0120044 "
    "Ek0200044 Ek0210044 Ek0300044 Ek1000044 Ek1001044 Ek1002044 Ek1010044 "
    "Ek1100044 Ek1110044 Ek1200044 Ek2000005 Ek2010044 Ek2100044 Ek3000040 "
    "El0000007 El0001044 El0003044 El0010002 El0011044 El0012044 El0020044 "
    "El0021044 El0100058 El0101044 El0102067 El0110044 El0111044 El0120044 "
    "El0200044 El0201044 El0210044 El0300044 El1000044 El1001044 El1010044 "
    "El1011044 El1020044 El1100044 El1101044 El1110044 El1200044 El2000044 "
    "El2001044 El2010044 El2100044 Em0000044 Em0001044 Em0002044 Em0003044 "
    "Em0010044 Em0011044 Em0012044 Em0020044 Em0021044 Em0030044 Em0100044 "
    "Em0101044 Em0102044 Em0110044 Em0111044 Em0120044 Em0200044 Em0201052 "
    "Em0210044 Em0300044 Em1000044 Em1001044 Em1002044 Em1010044 Em1100044 "
    "Em1110044 Em1200044 Em2000004 Em2010044 Em2100044 En0000013 En0001044 "
    "En0002049 En0003044 En0010018 En0011044 En0012044 En0020044 En0021044 "
    "En0100033 En0101044 En0102034 En0110044 En0111044 En0120044 En0200044 "
    "En0201044 En0210044 En0300044 En1000044 En1001044 En1002041 En1010044 "
    "En1011044 En1020044 En1100044 En1101044 En1110044 En1200044 En2000044 "
    "En2001044 En2010044 En2100044 En3000029 Eo0000044 Eo0001044 Eo0002044 "
    "Eo0003044 Eo0010044 Eo0011044 Eo0012044 Eo0020044 Eo0021044 Eo0030044 "
    "Eo0100044 Eo0101044 Eo0102044 Eo0110044 Eo0111044 Eo0120044 Eo0200044 "
    "Eo0201069 Eo0210044 Eo0300044 Eo1000044 Eo1001044 Eo1002044 Eo1010044 "
    "Eo1100044 Eo1101066 Eo1110044 Eo1200044 Eo2000076 Eo2010044 Eo2100044 "
    "Eo3000065 Ep0000058 Ep0001044 Ep0002032 Ep0003044 Ep0010014 Ep0011044 "
    "Ep0012044 Ep0020044 Ep0021044 Ep0100048 Ep0101044 Ep0102003 Ep0110044 "
    "Ep0111044 Ep0120044 Ep0200044 Ep0201044 Ep0210044 Ep0300044 Ep1000044 "
    "Ep1001044 Ep1002046 Ep1010044 Ep1011044 Ep1020044 Ep1100044 Ep1101044 "
    "Ep1110044 Ep1200044 Ep2000044 Ep2001044 Ep2010044 Ep2100044 Ep3000066 "
    "Eq0000044 Eq0001044 Eq0002044 Eq0003044 Eq0010044 Eq0011044 Eq0012044 "
    "Eq0020044 Eq0021044 Eq0030044 Eq0100044 Eq0101044 Eq0102044 Eq0110044 "
    "Eq0111044 Eq0120044 Eq0200044 Eq0210044 Eq0300044 Eq1000044 Eq1001044 "
    "Eq1002044 Eq1010044 Eq1100044 Eq1110044 Eq1200044 Eq2000041 Eq2010044 "
    "Eq2100044 Er0000079 Er0001044 Er0002013 Er0003044 Er0010017 Er0011044 "
    "Er0012044 Er0020044 Er0021044 Er0100070 Er0101044 Er0110044 Er0111044 "
    "Er0120044 Er0200044 Er0201044 Er0210044 Er0300044 Er1000044 Er1001044 "
    "Er1010044 Er1011044 Er1020044 Er1100044 Er1101044 Er1110044 Er1200044 "
    "Er2000044 Er2001044 Er2010044 Er2100044 Es0000044 Es0001044 Es0002044 "
    "Es0003044 Es0010044 Es0011044 Es0012044 Es0020044 Es0021044 Es0030044 "
    "Es0100044 Es0101044 Es0102044 Es0110044 Es0111044 Es0120044 Es0200044 "
    "Es0210044 Es0300044 Es1000044 Es1001044 Es1002044 Es1010044 Es1100044 "
    "Es1110044 Es1200044 Es2010044 Es2100044 Et0000030 Et0001044 Et0003044 "
    "Et0010031 Et0011044 Et0012044 Et0020080 Et0021080 Et0100051 Et0101080 "
    "Et0110080 Et0111080 Et0120080 Et0200080 Et0201080 Et0210080 Et0300080 "
    "Et1000080 Et1001080 Et1010080 Et1011080 Et1020080 Et1100080 Et1101080 "
    "Et1110080 Et1200080 Et2000080 Et2001080 Et2010080 Et2100080 Eu0000080 "
    "Eu0001080 Eu0002080 Eu0003080 Eu0010080 Eu0011080 Eu0012080 Eu0020080 "
    "Eu0021080 Eu0030080 Eu0100080 Eu0101080 Eu0102080 Eu0110080 Eu0111080 "
    "Eu0120080 Eu0200080 Eu0201007 Eu0210080 Eu0300080 Eu1000080 Eu1001080 "
    "Eu1002080 Eu1010080 Eu1100080 Eu1101059 Eu1110080 Eu1200080 Eu2000048 "
    "Eu2001008 Eu2010080 Eu2100080 Eu3000039 Ev0000066 Ev0001080 Ev0002034 "
    "Ev0003080 Ev0010013 Ev0011080 Ev0012080 Ev0020080 Ev0021080 Ev0100078 "
    "Ev0101080 Ev0102013 Ev0110080 Ev0111080 Ev0120080 Ev0200080 Ev0201080 "
    "Ev0210080 Ev0300080 Ev1000080 Ev1001080 Ev1010080 Ev1011080 Ev1020080 "
    "Ev1100080 Ev1101080 Ev1110080 Ev1200080 Ev2000080 Ev2001080 Ev2010080 "
    "Ev2100080 Ev3000055 Ew0000080 Ew0001080 Ew0002080 Ew0003080 Ew0010055 "
    "Ew0011055 Ew0012055 Ew0020055 Ew0021055 Ew0030055 Ew0100055 Ew0101055 "
    "Ew0102055 Ew0110055 Ew0111055 Ew0120055 Ew0200068 Ew0210068 Ew0300068 "
    "Ew1000006 Ew1001006 Ew1002006 Ew1010027 Ew1100018 Ew1110018 Ew1200018 "
    "Ew2010018 Ew2100018 Ex0000015 Ex0001018 Ex0002012 Ex0003018 Ex0010003 "
    "Ex0011018 Ex0012018 Ex0020018 Ex0021018 Ex0100052 Ex0101018 Ex0102076 "
    "Ex0110018 Ex0111018 Ex0120018 Ex0200018 Ex0201018 Ex0210018 Ex0300018 "
    "Ex1000018 Ex1001018 Ex1002032 Ex1010018 Ex1011018 Ex1020018 Ex1100018 "
    "Ex1101018 Ex1110018 Ex1200018 Ex2000018 Ex2001018 Ex2010018 Ex2100018 "
    "Ex3000036 "
)

CERT_L5_R0 = (
    "Sa0000036 Sa0001055 Sa0002038 Sa0003044 Sa0010005 Sa0011069 Sa0020077 "
    "Sa0100058 Sa0101019 Sa0110016 Sa0200074 Sa1000054 Sa1001061 Sa1010020 "
    "Sa1100006 Sb0000058 Sb0001039 Sb0002008 Sb0003023 Sb0010033 Sb0011028 "
    "Sb0012037 Sb0020047 Sb0100032 Sb0101016 Sb0102025 Sb0110021 Sb0111041 "
    "Sb0200021 Sb0201048 Sb1000014 Sb1001009 Sb1010080 Sb1100004 Sc0000072 "
    "Sc0001071 Sc0002016 Sc0003055 Sc0010012 Sc0011011 Sc0020071 Sc0100052 "
    "Sc0101015 Sc0102057 Sc0110032 Sc0200073 Sc0210003 Sc1000049 Sc1001010 "
    "Sc1010049 Sc1100005 Sd0000073 Sd0001062 Sd0002007 Sd0010014 Sd0011017 "
    "Sd0020015 Sd0100077 Sd0101029 Sd0102022 Sd0110048 Sd0200019 Sd1000058 "
    "Sd1001011 Sd1010037 Sd1100067 Se0000027 Se0001045 Se0002022 Se0003004 "
    "Se0010076 Se0011066 Se0020008 Se0100007 Se0101032 Se0102064 Se0110061 "
    "Se0111003 Se0200037 Se0201080 Se1000030 Se1001046 Se1010054 Se1100052 "
    "Sf0000026 Sf0001077 Sf0010023 Sf0011015 Sf0020045 Sf0100067 Sf0101071 "
    "Sf0110044 Sf0200071 Sf1000046 Sf1010072 Sf1100015 Sh0100027 Si0000042 "
    "Si0001047 Si0002056 Si0003026 Si0010073 Si0011006 Si0020058 Si0100007 "
    "Si0101025 Si0102011 Si0110066 Si0200022 Si1000004 Si1001029 Si1010066 "
    "Si1100058 Sj0000052 Sj0001047 Sj0002015 Sj0003034 Sj0010007 Sj0011025 "
    "Sj0012069 Sj0020075 Sj0100009 Sj0101065 Sj0102035 Sj0110055 Sj0200059 "
    "Sj1000029 Sj1001065 Sj1010036 Sj1100078 Sk0000037 Sk0001054 Sk0002057 "
    "Sk0010007 Sk0011029 Sk0020068 Sk0100035 Sk0101061 Sk0102034 Sk0110071 "
    "Sk0200006 Sk1000029 Sk1010045 Sk1100069 Sl0000062 Sl0001062 Sl0002053 "
    "Sl0010059 Sl0011037 Sl0020009 Sl0100011 Sl0101078 Sl0110064 Sl0200050 "
    "Sl1000038 Sl1010012 Sl1100020 Sm0000063 Sn0100025 Sp0000049 Sp0001058 "
    "Sp0002056 Sp0010011 Sp0011027 Sp0020002 Sp0100048 Sp0101031 Sp0102080 "
    "Sp0110015 Sp0200072 Sp0210057 Sp1000005 Sp1001044 Sp1010061 Sp1100048 "
    "Sq0100018 Sr0000050 Sr0001039 Sr0010058 Sr0011074 Sr0020019 Sr0100075 "
    "Sr0101028 Sr0110062 Sr0200013 Sr0210067 Sr1000038 Su0100054 Sw0100006 "
    "Sx0000043 Ua0000031 Ua0010046 Ua0011060 Ua0020060 Ua0100019 Ua0101015 "
    "Ua0110021 Ua0200072 Ua1000036 Ua1010024 Ua1100044 Ub0001077 Ub0010030 "
    "Ub0011058 Ub0020039 Ub0100028 Ub0101003 Ub0110033 Ub0200018 Ub1000047 "
    "Ub1010006 Ub1100023 Uc0000034 Uc0001058 Uc0002012 Uc0010039 Uc0011080 "
    "Uc0020069 Uc0021001 Uc0100002 Uc0101017 Uc0102075 Uc0110057 Uc0200037 "
    "Uc0201033 Uc1000042 Uc1010078 Uc1100020 Ud0000024 Ud0001040 Ud0010060 "
    "Ud0011025 Ud0020002 Ud0100078 Ud0101061 Ud0200046 Ud1000040 Ud1010055 "
    "Ud1100052 Ue0000009 Ue0001029 Ue0010011 Ue0011044 Ue0020022 Ue0100013 "
    "Ue0101034 Ue0200015 Ue1100034 Uf0000026 Uf0001041 Uf0010045 Uf0011046 "
    "Uf0020058 Uf0100067 Uf0101068 Uf0200008 Uf1002017 Ug0201056 Ug1011009 "
    "Ug1020001 Ug2000038 Ug3000036 Uh0000045 Uh0002016 Uh0100065 Ui1101060 "
    "Ui2000065 Ui3000013 Uj0002047 Uj0010075 Uj0100014 Uj0102024 Uj1002028 "
    "Uk1011030 Uk1101022 Uk2000010 Ul0000040 Ul0002031 Ul0030029 Ul0100017 "
    "Ul0102050 Ul1002033 Ul3000058 Um0201026 Um1101013 Um3000052 Un0000001 "
    "Un0010035 Uo1011041 Uo1101071 Uo2000038 Uo3000015 Up0000008 Up0002055 "
    "Up0010012 Up0100041 Up0102001 Up3000047 Uq1011036 Uq1101072 Uq2000015 "
    "Uq3000027 Ur0000025 Ur0002079 Ur0100063 Ut0000014 Ut0002018 Ut0010067 "
    "Uu1011048 Uu1101002 Uu2000073 Uu3000041 Uw0201023 Uw1011076 Uw1101008 "
    "Uw2000039 Uw3000021 Ux0000004 Ux0002055 Ux0010069 Ux0100033 Ux0102065 "
    "Ux1000068 Ux1001068 Ux1010068 Ux1011068 Ux1020068 Ux1100068 Ux1101068 "
    "Ux1110068 Ux1200068 Ux2000068 Ux2001068 Ux2010068 Ux2100068 Ea0000068 "
    "Ea0001068 Ea0002068 Ea0003068 Ea0010068 Ea0011068 Ea0012068 Ea0020068 "
    "Ea0021068 Ea0030068 Ea0100068 Ea0101068 Ea0102068 Ea0110068 Ea0111068 "
    "Ea0120068 Ea0200068 Ea0210068 Ea0300068 Ea1000068 Ea1001068 Ea1002068 "
    "Ea1010068 Ea1011016 Ea1100068 Ea1110068 Ea1200068 Ea2010068 Ea2100068 "
    "Eb0000036 Eb0001068 Eb0002060 Eb0003068 Eb0010045 Eb0011068 Eb0012068 "
    "Eb0020068 Eb0021068 Eb0100037 Eb0101068 Eb0110068 Eb0111068 Eb0120068 "
    "Eb0200068 Eb0201068 Eb0210068 Eb0300068 Eb1000068 Eb1001068 Eb1010068 "
    "Eb1011068 Eb1020068 Eb1100068 Eb1101068 Eb1110068 Eb1200068 Eb2000068 "
    "Eb2001068 Eb2010068 Eb2100068 Ec0000068 Ec0001068 Ec0002068 Ec0003068 "
    "Ec0010068 Ec0011068 Ec0012068 Ec0020068 Ec0021068 Ec0030068 Ec0100068 "
    "Ec0101068 Ec0102068 Ec0110068 Ec0111068 Ec0120068 Ec0200068 Ec0201033 "
    "Ec0210068 Ec0300068 Ec1000068 Ec1001068 Ec1002068 Ec1010068 Ec1011035 "
    "Ec1100068 Ec1101017 Ec1110068 Ec1200068 Ec2000054 Ec2010068 Ec2100068 "
    "Ec3000048 Ed0000013 Ed0001068 Ed0002056 Ed0003068 Ed0010030 Ed0011068 "
    "Ed0012068 Ed0020068 Ed0021068 Ed0100078 Ed0101068 Ed0110068 Ed0111068 "
    "Ed0120068 Ed0200068 Ed0201068 Ed0210068 Ed0300068 Ed1000068 Ed1001068 "
    "Ed1010068 Ed1011068 Ed1020068 Ed1100068 Ed1101068 Ed1110068 Ed1200068 "
    "Ed2000068 Ed2001068 Ed2010068 Ed2100068 Ed3000045 Ee0000068 Ee0001068 "
    "Ee0002068 Ee0003068 Ee0010068 Ee0011068 Ee0012068 Ee0020068 Ee0021068 "
    "Ee0030068 Ee0100068 Ee0101068 Ee0102068 Ee0110068 Ee0111068 Ee0120068 "
    "Ee0200068 Ee0210068 Ee0300068 Ee1000068 Ee1001068 Ee1002068 Ee1010068 "
    "Ee1100068 Ee1110068 Ee1200068 Ee2010068 Ee2100068 Ef0000023 Ef0001068 "
    "Ef0003068 Ef0010054 Ef0011068 Ef0012068 Ef0020068 Ef0021068 Ef0100079 "
    "Ef0101068 Ef0110068 Ef0111068 Ef0120068 Ef0200068 Ef0201068 Ef0210068 "
    "Ef0300068 Ef1000068 Ef1001068 Ef1010068 Ef1011068 Ef1020068 Ef1100068 "
    "Ef1101068 Ef1110068 Ef1200068 Ef2000068 Ef2001068 Ef2010068 Ef2100068 "
    "Eg0000068 Eg0001068 Eg0002068 Eg0003068 Eg0010068 Eg0011068 Eg0012068 "
    "Eg0020068 Eg0021068 Eg0030068 Eg0100068 Eg0101068 Eg0102068 Eg0110068 "
    "Eg0111068 Eg0120068 Eg0200068 Eg0210068 Eg0300068 Eg1000068 Eg1001068 "
    "Eg1002068 Eg1010068 Eg1100068 Eg1110068 Eg1200068 Eg2010068 Eg2100068 "
    "Eh0000013 Eh0001068 Eh0003068 Eh0010065 Eh0011068 Eh0012068 Eh0020068 "
    "Eh0021068 Eh0101068 Eh0110068 Eh0111068 Eh0120068 Eh0200068 Eh0201068 "
    "Eh0210068 Eh0300068 Eh1000068 Eh1001068 Eh1010068 Eh1011068 Eh1020068 "
    "Eh1100068 Eh1101068 Eh1110068 Eh1200068 Eh2000068 Eh2001068 Eh2010068 "
    "Eh2100068 Ei0000068 Ei0001068 Ei0002068 Ei0003068 Ei0010068 Ei0011068 "
    "Ei0012068 Ei0020068 Ei0021068 Ei0030068 Ei0100068 Ei0101068 Ei0102068 "
    "Ei0110068 Ei0111068 Ei0120068 Ei0200068 Ei0201051 Ei0210068 Ei0300068 "
    "Ei1000068 Ei1001068 Ei1002068 Ei1010068 Ei1011009 Ei1100068 Ei1101061 "
    "Ei1110068 Ei1200068 Ei2000003 Ei2010068 Ei2100068 Ei3000041 Ej0000078 "
    "Ej0001068 Ej0002003 Ej0003068 Ej0010080 Ej0011068 Ej0012068 Ej0020068 "
    "Ej0021068 Ej0100046 Ej0101068 Ej0102006 Ej0110068 Ej0111068 Ej0120068 "
    "Ej0200068 Ej0201068 Ej0210068 Ej0300068 Ej1000068 Ej1001068 Ej1010068 "
    "Ej1011068 Ej1020068 Ej1100068 Ej1101068 Ej1110068 Ej1200068 Ej2000068 "
    "Ej2001068 Ej2010068 Ej2100068 Ek0000068 Ek0001068 Ek0002068 Ek0003068 "
    "Ek0010068 Ek0011068 Ek0012068 Ek0020068 Ek0021068 Ek0030068 Ek0100068 "
    "Ek0101068 Ek0102068 Ek0110068 Ek0111068 Ek0120068 Ek0200068 Ek0210068 "
    "Ek0300068 Ek1000068 Ek1001068 Ek1002068 Ek1010068 Ek1011011 Ek1100068 "
    "Ek1110068 Ek1200068 Ek2000064 Ek2010068 Ek2100068 Ek3000079 El0000048 "
    "El0001068 El0002078 El0003068 El0010074 El0011068 El0012068 El0020068 "
    "El0021068 El0101068 El0102061 El0110068 El0111068 El0120068 El0200068 "
    "El0201068 El0210068 El0300068 El1000068 El1001068 El1010068 El1011068 "
    "El1020068 El1100068 El1101068 El1110068 El1200068 El2000068 El2001068 "
    "El2010068 El2100068 Em0000068 Em0001068 Em0002068 Em0003068 Em0010068 "
    "Em0011068 Em0012068 Em0020068 Em0021068 Em0030068 Em0100068 Em0101068 "
    "Em0102068 Em0110068 Em0111068 Em0120068 Em0200068 Em0201052 Em0210068 "
    "Em0300068 Em1000068 Em1001068 Em1002068 Em1010068 Em1011016 Em1100068 "
    "Em1101053 Em1110068 Em1200068 Em2000060 Em2010068 Em2100068 En0000001 "
    "En0001068 En0002031 En0003068 En0010044 En0011068 En0012068 En0020068 "
    "En0021068 En0100003 En0101068 En0102069 En0110068 En0111068 En0120068 "
    "En0200068 En0201068 En0210068 En0300068 En1000068 En1001068 En1010068 "
    "En1011068 En1020068 En1100068 En1101068 En1110068 En1200068 En2000068 "
    "En2001068 En2010068 En2100068 En3000045 Eo0000068 Eo0001068 Eo0002068 "
    "Eo0003068 Eo0010068 Eo0011068 Eo0012068 Eo0020068 Eo0021068 Eo0030068 "
    "Eo0100068 Eo0101068 Eo0102068 Eo0110068 Eo0111068 Eo0120068 Eo0200068 "
    "Eo0201046 Eo0210068 Eo0300068 Eo1000068 Eo1001068 Eo1002068 Eo1010068 "
    "Eo1011064 Eo1100068 Eo1101040 Eo1110068 Eo1200068 Eo2000030 Eo2010068 "
    "Eo2100068 Eo3000063 Ep0000012 Ep0001068 Ep0002006 Ep0003068 Ep0010006 "
    "Ep0011068 Ep0012068 Ep0020068 Ep0021068 Ep0100080 Ep0101068 Ep0102019 "
    "Ep0110068 Ep0111068 Ep0120068 Ep0200068 Ep0201068 Ep0210068 Ep0300068 "
    "Ep1000068 Ep1001068 Ep1010068 Ep1011068 Ep1020068 Ep1100068 Ep1101068 "
    "Ep1110068 Ep1200068 Ep2000068 Ep2001068 Ep2010068 Ep2100068 Ep3000055 "
    "Eq0000068 Eq0001068 Eq0002068 Eq0003068 Eq0010068 Eq0011068 Eq0012068 "
    "Eq0020068 Eq0021068 Eq0030068 Eq0100068 Eq0101068 Eq0102068 Eq0110068 "
    "Eq0111068 Eq0120068 Eq0200068 Eq0210068 Eq0300068 Eq1000068 Eq1001068 "
    "Eq1002068 Eq1010068 Eq1100068 Eq1110068 Eq1200068 Eq2000071 Eq2010068 "
    "Eq2100068 Er0000035 Er0001068 Er0002018 Er0003068 Er0010021 Er0011068 "
    "Er0012068 Er0020068 Er0021068 Er0100014 Er0101068 Er0110068 Er0111068 "
    "Er0120068 Er0200068 Er0201068 Er0210068 Er0300068 Er1000068 Er1001068 "
    "Er1010068 Er1011068 Er1020068 Er1100068 Er1101068 Er1110068 Er1200068 "
    "Er2000068 Er2001068 Er2010068 Er2100068 Es0000068 Es0001068 Es0002068 "
    "Es0003068 Es0010068 Es0011068 Es0012068 Es0020068 Es0021068 Es0030068 "
    "Es0100068 Es0101068 Es0102068 Es0110068 Es0111068 Es0120068 Es0200068 "
    "Es0210068 Es0300068 Es1000068 Es1001068 Es1002068 Es1010068 Es1100068 "
    "Es1110068 Es1200068 Es2010068 Es2100068 Et0000058 Et0001068 Et0003068 "
    "Et0010074 Et0011068 Et0012068 Et0020056 Et0021063 Et0100004 Et0101063 "
    "Et0110063 Et0111063 Et0120063 Et0200063 Et0201063 Et0210063 Et0300063 "
    "Et1000063 Et1001063 Et1010063 Et1011063 Et1020063 Et1100063 Et1101063 "
    "Et1110063 Et1200063 Et2000063 Et2001063 Et2010063 Et2100063 Eu0000063 "
    "Eu0001063 Eu0002063 Eu0003063 Eu0010063 Eu0011063 Eu0012063 Eu0020063 "
    "Eu0021063 Eu0030063 Eu0100063 Eu0101063 Eu0102063 Eu0110063 Eu0111063 "
    "Eu0120063 Eu0200063 Eu0201024 Eu0210063 Eu0300063 Eu1000063 Eu1001063 "
    "Eu1002063 Eu1010063 Eu1011012 Eu1100063 Eu1101013 Eu1110063 Eu1200063 "
    "Eu2000048 Eu2001028 Eu2010063 Eu2100063 Eu3000018 Ev0000031 Ev0001063 "
    "Ev0002031 Ev0003063 Ev0010055 Ev0011063 Ev0012063 Ev0020063 Ev0021063 "
    "Ev0100021 Ev0101063 Ev0102053 Ev0110063 Ev0111063 Ev0120063 Ev0200063 "
    "Ev0201063 Ev0210063 Ev0300063 Ev1000063 Ev1001063 Ev1002014 Ev1010063 "
    "Ev1011063 Ev1020063 Ev1100063 Ev1101063 Ev1110063 Ev1200063 Ev2000063 "
    "Ev2001063 Ev2010063 Ev2100063 Ev3000076 Ew0000063 Ew0001063 Ew0002063 "
    "Ew0003063 Ew0010031 Ew0011031 Ew0012031 Ew0020031 Ew0021031 Ew0030031 "
    "Ew0100031 Ew0101031 Ew0102031 Ew0110031 Ew0111031 Ew0120031 Ew0200055 "
    "Ew0210055 Ew0300055 Ew1000001 Ew1001001 Ew1002001 Ew1010068 Ew1100052 "
    "Ew1110052 Ew1200052 Ew2010052 Ew2100052 Ex0000046 Ex0001052 Ex0002032 "
    "Ex0003052 Ex0010018 Ex0011052 Ex0012052 Ex0020052 Ex0021052 Ex0100018 "
    "Ex0101052 Ex0102005 Ex0110052 Ex0111052 Ex0120052 Ex0200052 Ex0201052 "
    "Ex0210052 Ex0300052 Ex1000052 Ex1001052 Ex1010052 Ex1011052 Ex1020052 "
    "Ex1100052 Ex1101052 Ex1110052 Ex1200052 Ex2000052 Ex2001052 Ex2010052 "
    "Ex2100052 Ex3000009 "
)

CERT_L5_R1 = (
    "Sa0000015 Sa0001014 Sa0002030 Sa0010075 Sa0011059 Sa0012067 Sa0020032 "
    "Sa0100011 Sa0101078 Sa0102022 Sa0200039 Sa1000066 Sa1001026 Sa1010045 "
    "Sa1100054 Sb0000002 Sb0001009 Sb0002008 Sb0003079 Sb0010055 Sb0011020 "
    "Sb0020077 Sb0100042 Sb0101077 Sb0102011 Sb0110058 Sb0200065 Sb0201024 "
    "Sb1000072 Sb1001015 Sb1010050 Sb1100034 Sc0000077 Sc0001015 Sc0002036 "
    "Sc0003040 Sc0010058 Sc0011038 Sc0020032 Sc0100023 Sc0101075 Sc0102010 "
    "Sc0110011 Sc0200052 Sc1000051 Sc1001053 Sc1010047 Sc1100007 Sd0000035 "
    "Sd0001055 Sd0002026 Sd0003011 Sd0010021 Sd0011062 Sd0012077 Sd0020040 "
    "Sd0100054 Sd0101034 Sd0102054 Sd0110019 Sd0200051 Sd1000060 Sd1001046 "
    "Sd1010060 Sd1100077 Se0000016 Se0001013 Se0002062 Se0003078 Se0010035 "
    "Se0011053 Se0100033 Se0101057 Se0102036 Se0110078 Se0200068 Se0201012 "
    "Se1000042 Se1001071 Se1010057 Se1100048 Sf0000062 Sf0001039 Sf0010078 "
    "Sf0011019 Sf0020049 Sf0100032 Sf0101003 Sf0200053 Sf1000054 Sf1010016 "
    "Sf1100054 Si0000069 Si0001070 Si0002012 Si0003072 Si0010063 Si0011061 "
    "Si0012055 Si0020068 Si0100080 Si0101061 Si0102030 Si0110013 Si0200021 "
    "Si1000009 Si1001027 Si1010043 Si1100039 Sj0000062 Sj0001038 Sj0002010 "
    "Sj0003039 Sj0010066 Sj0011018 Sj0012051 Sj0020053 Sj0100044 Sj0101052 "
    "Sj0102075 Sj0110062 Sj0200024 Sj1000021 Sj1001044 Sj1010074 Sj1100022 "
    "Sk0000007 Sk0001033 Sk0002045 Sk0010049 Sk0011015 Sk0020041 Sk0100052 "
    "Sk0101080 Sk0110057 Sk0200041 Sk1000009 Sk1010067 Sk1100075 Sl0000005 "
    "Sl0001014 Sl0002001 Sl0010074 Sl0011073 Sl0020026 Sl0100014 Sl0101062 "
    "Sl0110047 Sl0200018 Sl1000012 Sl1010012 Sl1100045 Sm0000025 Sn0100041 "
    "Sp0000076 Sp0001060 Sp0002077 Sp0010034 Sp0011023 Sp0020002 Sp0101040 "
    "Sp0110075 Sp0200053 Sp1000064 Sp1001080 Sp1010008 Sp1100041 Sp1101015 "
    "Sq0100064 Sr0000018 Sr0001015 Sr0010057 Sr0011015 Sr0020078 Sr0100051 "
    "Sr0101074 Sr0110034 Sr0200066 Sr0201066 Sr1000015 Sr1101029 Su0100051 "
    "Sw0100078 Sx0000033 Ua0000007 Ua0010069 Ua0011021 Ua0020061 Ua0100072 "
    "Ua0101008 Ua0110073 Ua0200003 Ua1000027 Ua1010061 Ua1100068 Ub0000022 "
    "Ub0001051 Ub0010018 Ub0011079 Ub0020058 Ub0100016 Ub0101060 Ub0110074 "
    "Ub0200060 Ub1000060 Ub1010054 Ub1100072 Uc0000016 Uc0001072 Uc0002016 "
    "Uc0010053 Uc0011031 Uc0020004 Uc0100079 Uc0101003 Uc0102071 Uc0110014 "
    "Uc0200035 Uc0201029 Uc1010073 Uc1100080 Uc1101071 Ud0000029 Ud0001057 "
    "Ud0010045 Ud0011035 Ud0020047 Ud0100053 Ud0101072 Ud0200051 Ud1000059 "
    "Ud1010041 Ue0000057 Ue0001068 Ue0010053 Ue0011028 Ue0020013 Ue0100077 "
    "Ue0101012 Ue0200011 Ue1101076 Uf0000002 Uf0001074 Uf0002053 Uf0010078 "
    "Uf0011070 Uf0020046 Uf0030036 Uf0100021 Uf0101043 Uf0200002 Uf1002077 "
    "Ug0201063 Ug1020039 Ug1101030 Ug2000074 Ug2001027 Ug3000070 Uh0002021 "
    "Uh0100036 Uh0102029 Ui1101029 Ui2000073 Uj0002041 Uj0100005 Uj0102079 "
    "Uj1002053 Uk1011038 Uk1101077 Uk2000031 Uk3000061 Ul0000030 Ul0002053 "
    "Ul0100050 Ul0102062 Ul1002008 Um0201072 Um1101005 Un0000006 Un0002074 "
    "Un0010060 Uo1011063 Uo1101037 Uo2000038 Uo3000055 Up0000054 Up0002005 "
    "Up0010060 Up0100065 Uq1011035 Uq1101024 Uq2000063 Uq3000040 Ur0000061 "
    "Ur0002052 Ur0010031 Ur0100022 Us2000045 Ut0000026 Ut0002037 Ut0010062 "
    "Uu1011043 Uu1101069 Uu2000024 Uu3000016 Uw0201031 Uw1011031 Uw1101075 "
    "Uw2000055 Uw3000056 Ux0000077 Ux0002052 Ux0010008 Ux0100062 Ux0102003 "
    "Ux0200053 Ux0201053 Ux0210053 Ux0300053 Ux1000071 Ux1001071 Ux1010072 "
    "Ux1011072 Ux1020072 Ux1100072 Ux1101072 Ux1110072 Ux1200072 Ux2000072 "
    "Ux2001072 Ux2010072 Ux2100072 Ea0000072 Ea0001072 Ea0002072 Ea0003072 "
    "Ea0010072 Ea0011072 Ea0012072 Ea0020072 Ea0021072 Ea0030072 Ea0100072 "
    "Ea0101072 Ea0102072 Ea0110072 Ea0111072 Ea0120072 Ea0200072 Ea0210072 "
    "Ea0300072 Ea1000072 Ea1001072 Ea1002072 Ea1010072 Ea1011005 Ea1100072 "
    "Ea1101002 Ea1110072 Ea1200072 Ea2010072 Ea2100072 Eb0000009 Eb0001072 "
    "Eb0002078 Eb0003072 Eb0010051 Eb0011072 Eb0012072 Eb0020072 Eb0021072 "
    "Eb0100077 Eb0101072 Eb0110072 Eb0111072 Eb0120072 Eb0200072 Eb0201072 "
    "Eb0210072 Eb0300072 Eb1000072 Eb1001072 Eb1010072 Eb1011072 Eb1020072 "
    "Eb1100072 Eb1101072 Eb1110072 Eb1200072 Eb2000072 Eb2001072 Eb2010072 "
    "Eb2100072 Ec0000072 Ec0001072 Ec0002072 Ec0003072 Ec0010072 Ec0011072 "
    "Ec0012072 Ec0020072 Ec0021072 Ec0030072 Ec0100072 Ec0101072 Ec0102072 "
    "Ec0110072 Ec0111072 Ec0120072 Ec0200072 Ec0201066 Ec0210072 Ec0300072 "
    "Ec1000072 Ec1001072 Ec1002072 Ec1010072 Ec1011021 Ec1100072 Ec1101065 "
    "Ec1110072 Ec1200072 Ec2000072 Ec2010072 Ec2100072 Ed0000015 Ed0001072 "
    "Ed0002022 Ed0003072 Ed0010016 Ed0011072 Ed0012072 Ed0020072 Ed0021072 "
    "Ed0100077 Ed0101072 Ed0102052 Ed0110072 Ed0111072 Ed0120072 Ed0200072 "
    "Ed0201072 Ed0210072 Ed0300072 Ed1000072 Ed1001072 Ed1010072 Ed1011072 "
    "Ed1020072 Ed1100072 Ed1101072 Ed1110072 Ed1200072 Ed2000072 Ed2001072 "
    "Ed2010072 Ed2100072 Ee0000072 Ee0001072 Ee0002072 Ee0003072 Ee0010072 "
    "Ee0011072 Ee0012072 Ee0020072 Ee0021072 Ee0030072 Ee0100072 Ee0101072 "
    "Ee0102072 Ee0110072 Ee0111072 Ee0120072 Ee0200072 Ee0210072 Ee0300072 "
    "Ee1000072 Ee1001072 Ee1002072 Ee1010072 Ee1100072 Ee1110072 Ee1200072 "
    "Ee2010072 Ee2100072 Ef0000066 Ef0001072 Ef0003072 Ef0010065 Ef0011072 "
    "Ef0012072 Ef0020072 Ef0021072 Ef0100028 Ef0101072 Ef0110072 Ef0111072 "
    "Ef0120072 Ef0200072 Ef0201072 Ef0210072 Ef0300072 Ef1000072 Ef1001072 "
    "Ef1010072 Ef1011072 Ef1020072 Ef1100072 Ef1101072 Ef1110072 Ef1200072 "
    "Ef2000072 Ef2001072 Ef2010072 Ef2100072 Eg0000072 Eg0001072 Eg0002072 "
    "Eg0003072 Eg0010072 Eg0011072 Eg0012072 Eg0020072 Eg0021072 Eg0030072 "
    "Eg0100072 Eg0101072 Eg0102072 Eg0110072 Eg0111072 Eg0120072 Eg0200072 "
    "Eg0210072 Eg0300072 Eg1000072 Eg1001072 Eg1002072 Eg1010072 Eg1100072 "
    "Eg1110072 Eg1200072 Eg2010072 Eg2100072 Eh0000071 Eh0001072 Eh0003072 "
    "Eh0010015 Eh0011072 Eh0012072 Eh0020072 Eh0021072 Eh0100036 Eh0101072 "
    "Eh0110072 Eh0111072 Eh0120072 Eh0200072 Eh0201072 Eh0210072 Eh0300072 "
    "Eh1000072 Eh1001072 Eh1010072 Eh1011072 Eh1020072 Eh1100072 Eh1101072 "
    "Eh1110072 Eh1200072 Eh2000072 Eh2001072 Eh2010072 Eh2100072 Ei0000072 "
    "Ei0001072 Ei0002072 Ei0003072 Ei0010072 Ei0011072 Ei0012072 Ei0020072 "
    "Ei0021072 Ei0030072 Ei0100072 Ei0101072 Ei0102072 Ei0110072 Ei0111072 "
    "Ei0120072 Ei0200072 Ei0201060 Ei0210072 Ei0300072 Ei1000072 Ei1001072 "
    "Ei1002072 Ei1010072 Ei1011045 Ei1100072 Ei1101021 Ei1110072 Ei1200072 "
    "Ei2000077 Ei2010072 Ei2100072 Ei3000013 Ej0000058 Ej0001072 Ej0002048 "
    "Ej0003072 Ej0010010 Ej0011072 Ej0012072 Ej0020072 Ej0021072 Ej0100053 "
    "Ej0101072 Ej0102060 Ej0110072 Ej0111072 Ej0120072 Ej0200072 Ej0201072 "
    "Ej0210072 Ej0300072 Ej1000072 Ej1001072 Ej1002071 Ej1010072 Ej1011072 "
    "Ej1020072 Ej1100072 Ej1101072 Ej1110072 Ej1200072 Ej2000072 Ej2001072 "
    "Ej2010072 Ej2100072 Ek0000072 Ek0001072 Ek0002072 Ek0003072 Ek0010072 "
    "Ek0011072 Ek0012072 Ek0020072 Ek0021072 Ek0030072 Ek0100072 Ek0101072 "
    "Ek0102072 Ek0110072 Ek0111072 Ek0120072 Ek0200072 Ek0210072 Ek0300072 "
    "Ek1000072 Ek1001072 Ek1002072 Ek1010072 Ek1100072 Ek1101017 Ek1110072 "
    "Ek1200072 Ek2000034 Ek2010072 Ek2100072 Ek3000031 El0000048 El0001072 "
    "El0002023 El0003072 El0010008 El0011072 El0012072 El0020072 El0021072 "
    "El0100061 El0101072 El0102019 El0110072 El0111072 El0120072 El0200072 "
    "El0201072 El0210072 El0300072 El1000072 El1001072 El1010072 El1011072 "
    "El1020072 El1100072 El1101072 El1110072 El1200072 El2000072 El2001072 "
    "El2010072 El2100072 Em0000072 Em0001072 Em0002072 Em0003072 Em0010072 "
    "Em0011072 Em0012072 Em0020072 Em0021072 Em0030072 Em0100072 Em0101072 "
    "Em0102072 Em0110072 Em0111072 Em0120072 Em0200072 Em0201011 Em0210072 "
    "Em0300072 Em1000072 Em1001072 Em1002072 Em1010072 Em1100072 Em1101040 "
    "Em1110072 Em1200072 Em2000069 Em2010072 Em2100072 En0000012 En0001072 "
    "En0002061 En0003072 En0010030 En0011072 En0012072 En0020072 En0021072 "
    "En0100066 En0101072 En0102043 En0110072 En0111072 En0120072 En0200072 "
    "En0201072 En0210072 En0300072 En1000072 En1001072 En1002076 En1010072 "
    "En1011072 En1020072 En1100072 En1101072 En1110072 En1200072 En2000072 "
    "En2001072 En2010072 En2100072 En3000069 Eo0000072 Eo0001072 Eo0002072 "
    "Eo0003072 Eo0010072 Eo0011072 Eo0012072 Eo0020072 Eo0021072 Eo0030072 "
    "Eo0100072 Eo0101072 Eo0102072 Eo0110072 Eo0111072 Eo0120072 Eo0200072 "
    "Eo0201078 Eo0210072 Eo0300072 Eo1000072 Eo1001072 Eo1002072 Eo1010072 "
    "Eo1011058 Eo1100072 Eo1101011 Eo1110072 Eo1200072 Eo2000047 Eo2010072 "
    "Eo2100072 Eo3000027 Ep0000033 Ep0001072 Ep0002002 Ep0003072 Ep0010072 "
    "Ep0011072 Ep0012072 Ep0020072 Ep0021072 Ep0100072 Ep0101072 Ep0102045 "
    "Ep0110072 Ep0111072 Ep0120072 Ep0200072 Ep0201072 Ep0210072 Ep0300072 "
    "Ep1000072 Ep1001072 Ep1002080 Ep1010072 Ep1011072 Ep1020072 Ep1100072 "
    "Ep1101072 Ep1110072 Ep1200072 Ep2000072 Ep2001072 Ep2010072 Ep2100072 "
    "Ep3000020 Eq0000072 Eq0001072 Eq0002072 Eq0003072 Eq0010072 Eq0011072 "
    "Eq0012072 Eq0020072 Eq0021072 Eq0030072 Eq0100072 Eq0101072 Eq0102072 "
    "Eq0110072 Eq0111072 Eq0120072 Eq0200072 Eq0210072 Eq0300072 Eq1000072 "
    "Eq1001072 Eq1002072 Eq1010072 Eq1100072 Eq1110072 Eq1200072 Eq2000066 "
    "Eq2010072 Eq2100072 Er0000056 Er0001072 Er0002038 Er0003072 Er0010017 "
    "Er0011072 Er0012072 Er0020072 Er0021072 Er0100030 Er0101072 Er0110072 "
    "Er0111072 Er0120072 Er0200072 Er0201072 Er0210072 Er0300072 Er1000072 "
    "Er1001072 Er1010072 Er1011072 Er1020072 Er1100072 Er1101072 Er1110072 "
    "Er1200072 Er2000072 Er2001072 Er2010072 Er2100072 Es0000072 Es0001072 "
    "Es0002072 Es0003072 Es0010072 Es0011072 Es0012072 Es0020072 Es0021072 "
    "Es0030072 Es0100072 Es0101072 Es0102072 Es0110072 Es0111072 Es0120072 "
    "Es0200072 Es0210072 Es0300072 Es1000072 Es1001072 Es1002072 Es1010072 "
    "Es1100072 Es1110072 Es1200072 Es2010072 Es2100072 Et0000007 Et0001072 "
    "Et0003072 Et0010051 Et0011018 Et0012018 Et0020063 Et0021036 Et0100033 "
    "Et0101036 Et0110036 Et0111036 Et0120036 Et0200036 Et0201036 Et0210036 "
    "Et0300036 Et1000036 Et1001036 Et1010036 Et1011036 Et1020036 Et1100036 "
    "Et1101036 Et1110036 Et1200036 Et2000036 Et2001036 Et2010036 Et2100036 "
    "Eu0000036 Eu0001036 Eu0002036 Eu0003036 Eu0010036 Eu0011036 Eu0012036 "
    "Eu0020036 Eu0021036 Eu0030036 Eu0100036 Eu0101036 Eu0102036 Eu0110036 "
    "Eu0111036 Eu0120036 Eu0200036 Eu0201033 Eu0210036 Eu0300036 Eu1000036 "
    "Eu1001036 Eu1002036 Eu1010036 Eu1100036 Eu1101061 Eu1110036 Eu1200036 "
    "Eu2000027 Eu2010036 Eu2100036 Eu3000059 Ev0000062 Ev0001036 Ev0002029 "
    "Ev0003036 Ev0010080 Ev0011036 Ev0012036 Ev0020036 Ev0021036 Ev0100019 "
    "Ev0101036 Ev0102002 Ev0110036 Ev0111036 Ev0120036 Ev0200036 Ev0201036 "
    "Ev0210036 Ev0300036 Ev1000036 Ev1001036 Ev1002057 Ev1010036 Ev1011036 "
    "Ev1020036 Ev1100036 Ev1101036 Ev1110036 Ev1200036 Ev2000036 Ev2001036 "
    "Ev2010036 Ev2100036 Ev3000017 Ew0000036 Ew0001036 Ew0002036 Ew0003036 "
    "Ew0010052 Ew0011052 Ew0012052 Ew0020052 Ew0021052 Ew0030052 Ew0100052 "
    "Ew0101052 Ew0102052 Ew0110052 Ew0111052 Ew0120052 Ew0200066 Ew0210066 "
    "Ew0300066 Ew1000027 Ew1001039 Ew1002039 Ew1010074 Ew1100045 Ew1110045 "
    "Ew1200045 Ew2010045 Ew2100045 Ex0000033 Ex0001045 Ex0002067 Ex0003045 "
    "Ex0010062 Ex0011045 Ex0012045 Ex0020045 Ex0021045 Ex0100040 Ex0101045 "
    "Ex0102037 Ex0110045 Ex0111045 Ex0120045 Ex0200045 Ex0201045 Ex0210045 "
    "Ex0300045 Ex1000045 Ex1001045 Ex1002035 Ex1010045 Ex1011045 Ex1020045 "
    "Ex1100045 Ex1101045 Ex1110045 Ex1200045 Ex2000045 Ex2001045 Ex2010045 "
    "Ex2100045 Ex3000007 "
)

CERT_L5_R2 = (
    "Sa0000069 Sa0001045 Sa0002028 Sa0003022 Sa0010053 Sa0011005 Sa0020041 "
    "Sa0100068 Sa0101069 Sa0102075 Sa0110040 Sa0200032 Sa1000078 Sa1001004 "
    "Sa1010028 Sa1100031 Sb0000015 Sb0001069 Sb0002054 Sb0003067 Sb0010074 "
    "Sb0011031 Sb0012016 Sb0020077 Sb0100025 Sb0101070 Sb0102035 Sb0110023 "
    "Sb0200008 Sb0201071 Sb1000014 Sb1001067 Sb1010015 Sb1100012 Sc0000053 "
    "Sc0001019 Sc0002078 Sc0003078 Sc0010067 Sc0011035 Sc0012022 Sc0020052 "
    "Sc0100080 Sc0101032 Sc0102076 Sc0110058 Sc0120029 Sc0200012 Sc0210079 "
    "Sc1000057 Sc1001069 Sc1010034 Sc1100077 Sd0000050 Sd0001069 Sd0002044 "
    "Sd0003044 Sd0010022 Sd0011009 Sd0012041 Sd0020002 Sd0100030 Sd0101020 "
    "Sd0102032 Sd0110047 Sd0111078 Sd0200048 Sd1000039 Sd1001058 Sd1010061 "
    "Sd1100054 Se0000059 Se0001019 Se0002002 Se0003031 Se0010065 Se0011047 "
    "Se0012038 Se0020062 Se0100062 Se0101043 Se0102053 Se0110058 Se0120079 "
    "Se0200055 Se0201005 Se1000033 Se1001013 Se1010068 Se1100066 Sf0000028 "
    "Sf0001064 Sf0002058 Sf0010043 Sf0011028 Sf0020044 Sf0100009 Sf0110016 "
    "Sf1000043 Sf1010014 Sf1100031 Sg0100070 Sh0100041 Si0000018 Si0001010 "
    "Si0002065 Si0003021 Si0010072 Si0011037 Si0012057 Si0020065 Si0100075 "
    "Si0101048 Si0102024 Si0110068 Si0111059 Si0200071 Si1000070 Si1001062 "
    "Si1010050 Si1100078 Sj0000015 Sj0001064 Sj0002050 Sj0003018 Sj0010004 "
    "Sj0011080 Sj0012072 Sj0020002 Sj0100002 Sj0101002 Sj0102033 Sj0110042 "
    "Sj0111006 Sj0200032 Sj1000019 Sj1001035 Sj1010066 Sj1100073 Sk0000003 "
    "Sk0001076 Sk0002009 Sk0003011 Sk0010035 Sk0011054 Sk0020079 Sk0100043 "
    "Sk0102079 Sk0110036 Sk0200005 Sk1000071 Sk1001030 Sk1010025 Sk1100076 "
    "Sl0000071 Sl0001072 Sl0002010 Sl0003034 Sl0010020 Sl0011021 Sl0020030 "
    "Sl0100065 Sl0102021 Sl0110059 Sl0200010 Sl1000017 Sl1001006 Sl1010003 "
    "Sl1100070 Sm0000054 Sn0100065 Sp0000037 Sp0001051 Sp0002057 Sp0003048 "
    "Sp0010059 Sp0011009 Sp0020012 Sp0100016 Sp0102013 Sp0110055 Sp0200003 "
    "Sp0210069 Sp1000020 Sp1100055 Sq0100051 Sr0000036 Sr0100050 Sr1000017 "
    "Sr1100004 Ss0000009 St0000042 Su0100043 Sv0000021 Sw0100077 Sx0000067 "
    "Ua0000058 Ua0001001 Ua0002054 Ua0010038 Ua0100021 Ua0101071 Ua0110069 "
    "Ua1000018 Ua1010059 Ua1100050 Ub0000031 Ub0001063 Ub0002016 Ub0010050 "
    "Ub0020057 Ub0021014 Ub0100054 Ub1000019 Ub1010033 Ub1100057 Uc0000041 "
    "Uc0001079 Uc0002007 Uc0003019 Uc0010064 Uc0011035 Uc0020016 Uc0100047 "
    "Uc0101013 Uc0102059 Uc0110070 Uc0200021 Uc1000075 Uc1001070 Uc1010050 "
    "Uc1100005 Uc2000004 Ud0000057 Ud0001008 Ud0010055 Ud0011032 Ud0100022 "
    "Ud1001030 Ud1002003 Ud1010017 Ud1011079 Ud1100080 Ue0000060 Ue0001035 "
    "Ue0010075 Ue0011076 Ue0100011 Ue0101070 Ue0102074 Ue0110039 Ue0111074 "
    "Ue0120074 Ue0200074 Ue0201074 Ue0210074 Ue0300074 Ue1000016 Ue1001074 "
    "Ue1002074 Ue1010074 Ue1011074 Ue1020074 Ue1100006 Ue1101074 Ue1110074 "
    "Ue1200074 Ue2000074 Ue2001074 Ue2010074 Ue2100074 Ue3000074 Uf0000038 "
    "Uf0001074 Uf0002074 Uf0003074 Uf0010028 Uf0011014 Uf0012074 Uf0020074 "
    "Uf0021074 Uf0030074 Uf0100054 Uf0102074 Uf0110034 Uf0120074 Uf0200074 "
    "Uf0201074 Uf0210074 Uf0300074 Uf1000019 Uf1002063 Uf1010074 Uf1020074 "
    "Uf1100029 Uf1101074 Uf1110074 Uf1200074 Uf2000074 Uf2001074 Uf2010074 "
    "Uf2100074 Ug0000074 Ug0001074 Ug0002074 Ug0003074 Ug0010074 Ug0011074 "
    "Ug0012074 Ug0020074 Ug0021074 Ug0030074 Ug0100074 Ug0101036 Ug0102074 "
    "Ug0110074 Ug0111074 Ug0120074 Ug0200074 Ug0201074 Ug0210074 Ug0300074 "
    "Ug1000074 Ug1001074 Ug1002074 Ug1010074 Ug1011074 Ug1020074 Ug1100074 "
    "Ug1101074 Ug1110074 Ug2000074 Ug2001074 Ug2010074 Ug2100074 Ug3000074 "
    "Uh0000074 Uh0003074 Uh0010072 Uh0011074 Uh0012074 Uh0020057 Uh0030074 "
    "Uh0100074 Uh0101068 Uh0110074 Uh0120074 Uh0200048 Uh0201074 Uh0210074 "
    "Uh0300074 Uh1000074 Uh1001009 Uh1002006 Uh1010074 Uh1020074 Uh1100074 "
    "Uh1101074 Uh1110074 Uh1200074 Uh2000074 Uh2001074 Uh2010074 Uh2100074 "
    "Ui0000074 Ui0001074 Ui0002074 Ui0003074 Ui0010074 Ui0011074 Ui0012074 "
    "Ui0020074 Ui0021074 Ui0030074 Ui0100074 Ui0101078 Ui0102074 Ui0110074 "
    "Ui0111074 Ui0120074 Ui0200074 Ui0201074 Ui0210074 Ui0300074 Ui1000074 "
    "Ui1001074 Ui1002074 Ui1010074 Ui1011074 Ui1020074 Ui1100074 Ui1101074 "
    "Ui1110074 Ui1200077 Ui2000074 Ui2001074 Ui2010074 Ui2100074 Ui3000074 "
    "Uj0000074 Uj0001056 Uj0002007 Uj0003074 Uj0011074 Uj0012074 Uj0030074 "
    "Uj0100008 Uj0110074 Uj0120074 Uj0201074 Uj0210074 Uj0300074 Uj1000074 "
    "Uj1002024 Uj1010074 Uj1020074 Uj1100074 Uj1101074 Uj1110074 Uj1200074 "
    "Uj2000074 Uj2001074 Uj2010074 Uj2100074 Uk0000041 Uk0001074 Uk0002074 "
    "Uk0003074 Uk0010074 Uk0011074 Uk0012074 Uk0020074 Uk0021074 Uk0030074 "
    "Uk0100049 Uk0101028 Uk0102074 Uk0110074 Uk0111074 Uk0120074 Uk0200074 "
    "Uk0201074 Uk0210074 Uk0300074 Uk1000018 Uk1001074 Uk1002074 Uk1010074 "
    "Uk1011074 Uk1020074 Uk1100074 Uk1101074 Uk1110074 Uk1200067 Uk2000074 "
    "Uk2001074 Uk2010074 Uk2100074 Uk3000074 Ul0000074 Ul0001079 Ul0003074 "
    "Ul0010026 Ul0011074 Ul0012074 Ul0030074 Ul0100074 Ul0101058 Ul0110074 "
    "Ul0120074 Ul0201074 Ul0210074 Ul0300074 Ul1000043 Ul1001025 Ul1002021 "
    "Ul1010074 Ul1020074 Ul1100074 Ul1101074 Ul1110074 Ul1200074 Ul2000074 "
    "Ul2001074 Ul2010074 Ul2100074 Ul3000021 Um0000074 Um0001074 Um0002074 "
    "Um0003074 Um0010074 Um0011074 Um0012074 Um0020074 Um0021074 Um0030074 "
    "Um0100074 Um0101007 Um0102074 Um0110074 Um0111074 Um0120074 Um0200074 "
    "Um0201074 Um0210074 Um0300074 Um1000074 Um1001074 Um1002074 Um1010074 "
    "Um1011074 Um1020074 Um1100074 Um1101074 Um1110074 Um1200002 Um2000074 "
    "Um2001074 Um2010074 Um2100074 Um3000074 Un0000074 Un0001052 Un0003074 "
    "Un0011074 Un0012074 Un0030074 Un0100074 Un0110074 Un0120074 Un0201074 "
    "Un0210074 Un0300074 Un1000074 Un1010074 Un1020074 Un1100074 Un1101074 "
    "Un1110074 Un1200074 Un2000074 Un2001074 Un2010074 Un2100074 Un3000064 "
    "Uo0000074 Uo0001074 Uo0002074 Uo0003074 Uo0010074 Uo0011074 Uo0012074 "
    "Uo0020074 Uo0021074 Uo0030074 Uo0100074 Uo0101031 Uo0102074 Uo0110074 "
    "Uo0111074 Uo0120074 Uo0200074 Uo0201074 Uo0210074 Uo0300074 Uo1000074 "
    "Uo1001074 Uo1002074 Uo1010074 Uo1011074 Uo1020074 Uo1100074 Uo1101074 "
    "Uo1110074 Uo1200004 Uo2000074 Uo2001074 Uo2010074 Uo2100074 Uo3000074 "
    "Up0000074 Up0001060 Up0002060 Up0003074 Up0010079 Up0011074 Up0012074 "
    "Up0020057 Up0030074 Up0100074 Up0101068 Up0102058 Up0110074 Up0111042 "
    "Up0120074 Up0200055 Up0201074 Up0210074 Up0300074 Up1000074 Up1001007 "
    "Up1010074 Up1020074 Up1100074 Up1101074 Up1110074 Up1200074 Up2000074 "
    "Up2001074 Up2010074 Up2100074 Uq0000074 Uq0001074 Uq0002074 Uq0003074 "
    "Uq0010074 Uq0011074 Uq0012074 Uq0020074 Uq0021074 Uq0030074 Uq0100074 "
    "Uq0101010 Uq0102074 Uq0110074 Uq0111074 Uq0120074 Uq0200074 Uq0201074 "
    "Uq0210074 Uq0300074 Uq1000074 Uq1001074 Uq1002074 Uq1010074 Uq1011074 "
    "Uq1020074 Uq1100074 Uq1101074 Uq1110074 Uq2000074 Uq2001074 Uq2010074 "
    "Uq2100074 Uq3000074 Ur0000074 Ur0001024 Ur0003074 Ur0010041 Ur0011074 "
    "Ur0012074 Ur0030074 Ur0100074 Ur0101024 Ur0110074 Ur0120074 Ur0201074 "
    "Ur0210074 Ur0300074 Ur1000074 Ur1010074 Ur1020074 Ur1100074 Ur1101074 "
    "Ur1110074 Ur1200074 Ur2000074 Ur2001074 Ur2010074 Ur2100074 Us0000074 "
    "Us0001074 Us0002074 Us0003074 Us0010074 Us0011074 Us0012074 Us0020074 "
    "Us0021074 Us0030074 Us0100074 Us0102074 Us0110074 Us0111074 Us0120074 "
    "Us0200074 Us0201074 Us0210074 Us0300074 Us1000074 Us1001074 Us1002074 "
    "Us1010074 Us1011074 Us1020074 Us1100074 Us1101074 Us1110074 Us2000074 "
    "Us2001074 Us2010074 Us2100074 Us3000074 Ut0000074 Ut0003074 Ut0010010 "
    "Ut0011074 Ut0012074 Ut0020076 Ut0030074 Ut0100074 Ut0101027 Ut0110074 "
    "Ut0111050 Ut0120074 Ut0200041 Ut0201074 Ut0210074 Ut0300074 Ut1000074 "
    "Ut1001050 Ut1010074 Ut1020074 Ut1100074 Ut1101074 Ut1110074 Ut1200074 "
    "Ut2000074 Ut2001074 Ut2010074 Ut2100074 Ut3000013 Uu0000074 Uu0001074 "
    "Uu0002074 Uu0003074 Uu0010074 Uu0011074 Uu0012074 Uu0020074 Uu0021074 "
    "Uu0030074 Uu0100074 Uu0101068 Uu0102074 Uu0110074 Uu0111074 Uu0120074 "
    "Uu0200074 Uu0201074 Uu0210074 Uu0300074 Uu1000074 Uu1001074 Uu1002074 "
    "Uu1010074 Uu1011074 Uu1020074 Uu1100074 Uu1101074 Uu1110074 Uu2000074 "
    "Uu2001074 Uu2010074 Uu2100074 Uu3000074 Uv0000074 Uv0001052 Uv0003074 "
    "Uv0011074 Uv0012074 Uv0030074 Uv0100074 Uv0102067 Uv0110074 Uv0120074 "
    "Uv0201074 Uv0210074 Uv0300074 Uv1000074 Uv1002007 Uv1010074 Uv1020074 "
    "Uv1100074 Uv1101074 Uv1110074 Uv1200074 Uv2000074 Uv2001074 Uv2010074 "
    "Uv2100074 Uw0000074 Uw0001074 Uw0002074 Uw0003074 Uw0010074 Uw0011074 "
    "Uw0012074 Uw0020074 Uw0021074 Uw0030074 Uw0100074 Uw0102074 Uw0110074 "
    "Uw0111074 Uw0120074 Uw0200074 Uw0201074 Uw0210074 Uw0300074 Uw1000074 "
    "Uw1001074 Uw1002074 Uw1010074 Uw1011074 Uw1020074 Uw1100074 Uw1101074 "
    "Uw1110074 Uw1200033 Uw2000074 Uw2001074 Uw2010074 Uw2100074 Uw3000074 "
    "Ux0000074 Ux0001027 Ux0002065 Ux0003074 Ux0010057 Ux0011074 Ux0012074 "
    "Ux0020012 Ux0030074 Ux0100074 Ux0101004 Ux0110074 Ux0111073 Ux0120074 "
    "Ux0200074 Ux0201074 Ux0210074 Ux0300074 Ux1000074 Ux1001035 Ux1010074 "
    "Ux1020074 Ux1100074 Ux1101074 Ux1110074 Ux1200074 Ux2000074 Ux2001074 "
    "Ux2010074 Ux2100074 Ux3000039 Ea0000074 Ea0001074 Ea0002074 Ea0003074 "
    "Ea0010074 Ea0011074 Ea0012074 Ea0020074 Ea0021074 Ea0030074 Ea0100074 "
    "Ea0102074 Ea0110074 Ea0111074 Ea0120074 Ea0200074 Ea0201074 Ea0210074 "
    "Ea0300074 Ea1000074 Ea1001074 Ea1002074 Ea1010074 Ea1011074 Ea1020074 "
    "Ea1100074 Ea1101074 Ea1110074 Ea2000074 Ea2001074 Ea2010074 Ea2100074 "
    "Ea3000074 Eb0000074 Eb0001075 Eb0003074 Eb0010013 Eb0011074 Eb0012074 "
    "Eb0020041 Eb0030074 Eb0100074 Eb0110074 Eb0111008 Eb0120074 Eb0200066 "
    "Eb0201074 Eb0210074 Eb0300074 Eb1000074 Eb1001001 Eb1010074 Eb1020074 "
    "Eb1100074 Eb1101074 Eb1110074 Eb1200074 Eb2000074 Eb2001074 Eb2010074 "
    "Eb2100074 Ec0000074 Ec0001074 Ec0002074 Ec0003074 Ec0010074 Ec0011074 "
    "Ec0012074 Ec0020074 Ec0021074 Ec0030074 Ec0100074 Ec0102074 Ec0110074 "
    "Ec0111074 Ec0120074 Ec0200074 Ec0201074 Ec0210074 Ec0300074 Ec1000074 "
    "Ec1001074 Ec1002074 Ec1010074 Ec1011074 Ec1020074 Ec1100074 Ec1101074 "
    "Ec1110074 Ec1200038 Ec2000074 Ec2001074 Ec2010074 Ec2100074 Ec3000074 "
    "Ed0000074 Ed0001071 Ed0002002 Ed0003074 Ed0010008 Ed0011074 Ed0012074 "
    "Ed0020019 Ed0030074 Ed0100074 Ed0101052 Ed0102022 Ed0110074 Ed0120074 "
    "Ed0200021 Ed0201074 Ed0210074 Ed0300074 Ed1000074 Ed1001005 Ed1010074 "
    "Ed1020074 Ed1100074 Ed1101074 Ed1110074 Ed1200074 Ed2000074 Ed2001074 "
    "Ed2010074 Ed2100074 Ed3000079 Ee0000074 Ee0001074 Ee0002074 Ee0003074 "
    "Ee0010074 Ee0011074 Ee0012074 Ee0020074 Ee0021074 Ee0030074 Ee0100074 "
    "Ee0101023 Ee0102074 Ee0110074 Ee0111074 Ee0120074 Ee0200074 Ee0201074 "
    "Ee0210074 Ee0300074 Ee1000074 Ee1001074 Ee1002074 Ee1010074 Ee1011074 "
    "Ee1020074 Ee1100074 Ee1101074 Ee1110074 Ee2000074 Ee2001074 Ee2010074 "
    "Ee2100074 Ee3000074 Ef0000074 Ef0003074 Ef0010068 Ef0011074 Ef0012074 "
    "Ef0030074 Ef0100074 Ef0110074 Ef0120074 Ef0201074 Ef0210074 Ef0300074 "
    "Ef1000074 Ef1010074 Ef1020074 Ef1100074 Ef1101074 Ef1110074 Ef1200074 "
    "Ef2000074 Ef2001074 Ef2010074 Ef2100074 Eg0000074 Eg0001074 Eg0002074 "
    "Eg0003074 Eg0010074 Eg0011074 Eg0012074 Eg0020074 Eg0021074 Eg0030074 "
    "Eg0100074 Eg0102074 Eg0110074 Eg0111074 Eg0120074 Eg0200074 Eg0201074 "
    "Eg0210074 Eg0300074 Eg1000074 Eg1001074 Eg1002074 Eg1010074 Eg1011074 "
    "Eg1020074 Eg1100074 Eg1101074 Eg1110074 Eg2000074 Eg2001074 Eg2010074 "
    "Eg2100074 Eg3000074 Eh0000074 Eh0002007 Eh0003074 Eh0010022 Eh0011074 "
    "Eh0012074 Eh0030074 Eh0100074 Eh0110074 Eh0120074 Eh0201074 Eh0210074 "
    "Eh0300074 Eh1000074 Eh1002007 Eh1010074 Eh1020074 Eh1100074 Eh1101074 "
    "Eh1110074 Eh1200074 Eh2000074 Eh2001074 Eh2010074 Eh2100074 Ei0000074 "
    "Ei0001074 Ei0002074 Ei0003074 Ei0010074 Ei0011074 Ei0012074 Ei0020074 "
    "Ei0021074 Ei0030074 Ei0100074 Ei0101007 Ei0102074 Ei0110074 Ei0111074 "
    "Ei0120074 Ei0200074 Ei0201074 Ei0210074 Ei0300074 Ei1000074 Ei1001074 "
    "Ei1002074 Ei1010074 Ei1011074 Ei1020074 Ei1100074 Ei1101074 Ei1110074 "
    "Ei2000074 Ei2001074 Ei2010074 Ei2100074 Ei3000074 Ej0000074 Ej0001075 "
    "Ej0002051 Ej0003074 Ej0010001 Ej0011074 Ej0012074 Ej0020029 Ej0030074 "
    "Ej0100074 Ej0101033 Ej0110074 Ej0120074 Ej0200024 Ej0201074 Ej0210074 "
    "Ej0300074 Ej1000074 Ej1001015 Ej1010074 Ej1020074 Ej1100074 Ej1101074 "
    "Ej1110074 Ej1200074 Ej2000074 Ej2001074 Ej2010074 Ej2100074 Ej3000008 "
    "Ek0000074 Ek0001074 Ek0002074 Ek0003074 Ek0010074 Ek0011074 Ek0012074 "
    "Ek0020074 Ek0021074 Ek0030074 Ek0100074 Ek0102074 Ek0110074 Ek0111074 "
    "Ek0120074 Ek0200074 Ek0201074 Ek0210074 Ek0300074 Ek1000074 Ek1001074 "
    "Ek1002074 Ek1010074 Ek1011074 Ek1020074 Ek1100074 Ek1101074 Ek1110074 "
    "Ek2000074 Ek2001074 Ek2010074 Ek2100074 Ek3000074 El0000074 El0001048 "
    "El0003074 El0011074 El0012074 El0020049 El0030074 El0100074 El0101006 "
    "El0102080 El0110074 El0111058 El0120074 El0200061 El0201074 El0210074 "
    "El0300074 El1000074 El1001023 El1010074 El1020074 El1100074 El1101074 "
    "El1110074 El1200074 El2000074 El2001074 El2010074 El2100074 El3000070 "
    "Em0000074 Em0001074 Em0002074 Em0003074 Em0010074 Em0011074 Em0012074 "
    "Em0020074 Em0021074 Em0030074 Em0100074 Em0102074 Em0110074 Em0111074 "
    "Em0120074 Em0200074 Em0201074 Em0210074 Em0300074 Em1000074 Em1001074 "
    "Em1002074 Em1010074 Em1011074 Em1020074 Em1100074 Em1101074 Em1110074 "
    "Em1200008 Em2000074 Em2001074 Em2010074 Em2100074 Em3000074 En0000064 "
    "En0001067 En0002043 En0003064 En0010052 En0011064 En0012064 En0020025 "
    "En0030064 En0100064 En0101040 En0102007 En0110064 En0111074 En0120064 "
    "En0200021 En0201064 En0210064 En0300064 En1000064 En1001055 En1010064 "
    "En1020064 En1100064 En1101064 En1110064 En1200064 En2000064 En2001064 "
    "En2010064 En2100064 Eo0000064 Eo0001064 Eo0002064 Eo0003064 Eo0010064 "
    "Eo0011064 Eo0012064 Eo0020064 Eo0021064 Eo0030064 Eo0100064 Eo0101007 "
    "Eo0102064 Eo0110064 Eo0111064 Eo0120064 Eo0200064 Eo0201064 Eo0210064 "
    "Eo0300064 Eo1000064 Eo1001064 Eo1002064 Eo1010064 Eo1011064 Eo1020064 "
    "Eo1100064 Eo1101064 Eo1110064 Eo1200047 Eo2000064 Eo2001064 Eo2010064 "
    "Eo2100064 Eo3000064 Ep0000064 Ep0001039 Ep0002026 Ep0003064 Ep0010077 "
    "Ep0011064 Ep0012064 Ep0020063 Ep0030064 Ep0100064 Ep0102023 Ep0110064 "
    "Ep0111017 Ep0120064 Ep0200077 Ep0201064 Ep0210064 Ep0300064 Ep1000064 "
    "Ep1001028 Ep1002003 Ep1010064 Ep1020064 Ep1100064 Ep1101064 Ep1110064 "
    "Ep1200064 Ep2000064 Ep2001064 Ep2010064 Ep2100064 Ep3000010 Eq0000064 "
    "Eq0001064 Eq0002003 Eq0003003 Eq0010003 Eq0011003 Eq0012003 Eq0020003 "
    "Eq0021003 Eq0030003 Eq0100080 Eq0101033 Eq0102080 Eq0110080 Eq0111080 "
    "Eq0120080 Eq0200080 Eq0201080 Eq0210080 Eq0300080 Eq1000080 Eq1001080 "
    "Eq1002080 Eq1010080 Eq1011080 Eq1020080 Eq1100080 Eq1101080 Eq1110080 "
    "Eq2000080 Eq2001080 Eq2010080 Eq2100080 Eq3000080 Er0000080 Er0001039 "
    "Er0003080 Er0010003 Er0011080 Er0012080 Er0020039 Er0030080 Er0100079 "
    "Er0110079 Er0120079 Er0200023 Er0201079 Er0210079 Er0300079 Er1000079 "
    "Er1010079 Er1020079 Er1100079 Er1101079 Er1110079 Er1200079 Er2000079 "
    "Er2001079 Er2010079 Er2100079 Es0000079 Es0001079 Es0002079 Es0003079 "
    "Es0010079 Es0011079 Es0012079 Es0020079 Es0021079 Es0030079 Es0100079 "
    "Es0102079 Es0110079 Es0111079 Es0120079 Es0200079 Es0201079 Es0210079 "
    "Es0300079 Es1000005 Es1001005 Es1002005 Es1010005 Es1011005 Es1020005 "
    "Es1100005 Es1101005 Es1110005 Es2000005 Es2001005 Es2010005 Es2100005 "
    "Es3000005 Et0000070 Et0003070 Et0010046 Et0011070 Et0012070 Et0030070 "
    "Et0100035 Et0110035 Et0120035 Et0201035 Et0210035 Et0300035 Et1000027 "
    "Et1010027 Et1020027 Et1100030 Et1101030 Et1110030 Et1200030 Et2000014 "
    "Et2001014 Et2010014 Et2100014 Eu0000014 Eu0001014 Eu0002014 Eu0003014 "
    "Eu0010014 Eu0011014 Eu0012014 Eu0020014 Eu0021014 Eu0030014 Eu0100006 "
    "Eu0102006 Eu0110006 Eu0111006 Eu0120006 Eu0200006 Eu0201006 Eu0210006 "
    "Eu0300006 Eu1000006 Eu1001006 Eu1002006 Eu1010006 Eu1011006 Eu1020006 "
    "Eu1100006 Eu1101006 Eu1110006 Eu1200042 Eu2000006 Eu2001006 Eu2010006 "
    "Eu2100006 Eu3000006 Ev0000078 Ev0001037 Ev0002078 Ev0003078 Ev0010057 "
    "Ev0011078 Ev0012078 Ev0030078 Ev0100078 Ev0101035 Ev0110078 Ev0120078 "
    "Ev0200015 Ev0201078 Ev0210078 Ev0300078 Ev1000015 Ev1001060 Ev1010015 "
    "Ev1020015 Ev1100015 Ev1101015 Ev1110015 Ev1200015 Ev2000015 Ev2001015 "
    "Ev2010015 Ev2100015 Ev3000048 Ew0000028 Ew0001028 Ew0002028 Ew0003028 "
    "Ew0010028 Ew0011028 Ew0012028 Ew0020028 Ew0021028 Ew0030028 Ew0100014 "
    "Ew0101061 Ew0102014 Ew0110014 Ew0111014 Ew0120014 Ew0200014 Ew0201014 "
    "Ew0210014 Ew0300014 Ew1000024 Ew1001024 Ew1002024 Ew1010024 Ew1011024 "
    "Ew1020024 Ew1100062 Ew1101062 Ew1110062 Ew2000078 Ew2001078 Ew2010078 "
    "Ew2100078 Ew3000078 Ex0000009 Ex0001073 Ex0002064 Ex0003009 Ex0010050 "
    "Ex0011009 Ex0012009 Ex0020069 Ex0030009 Ex0100026 Ex0101074 Ex0110026 "
    "Ex0120026 Ex0200033 Ex0201026 Ex0210026 Ex0300026 Ex1000021 Ex1001001 "
    "Ex1010021 Ex1020021 Ex1100054 Ex1101054 Ex1110054 Ex1200054 Ex2000039 "
    "Ex2001039 Ex2010039 Ex2100039 Ex3000066 "
)

CERT_L11_R0 = (
    "Sa0000033 Sa0001034 Sa0002063 Sa0003021 Sa0010032 Sa0011064 Sa0100066 "
    "Sa0101058 Sa0102041 Sa0110079 Sa0200066 Sa1000024 Sa1001027 Sa1010072 "
    "Sa1100054 Sb0000004 Sb0001072 Sb0002018 Sb0003001 Sb0010032 Sb0011048 "
    "Sb0012011 Sb0020039 Sb0100012 Sb0101055 Sb0102055 Sb0110031 Sb0111075 "
    "Sb0200021 Sb0201012 Sb1000018 Sb1001076 Sb1010061 Sb1100005 Sc0000042 "
    "Sc0001010 Sc0002063 Sc0003002 Sc0010015 Sc0011005 Sc0020078 Sc0100073 "
    "Sc0101063 Sc0102019 Sc0110036 Sc0200062 Sc0210074 Sc1000060 Sc1001061 "
    "Sc1010046 Sc1100071 Sd0000067 Sd0001016 Sd0002062 Sd0010012 Sd0011035 "
    "Sd0020022 Sd0100020 Sd0101076 Sd0102028 Sd0110006 Sd0200077 Sd1000044 "
    "Sd1001064 Sd1010073 Sd1100004 Se0000073 Se0001065 Se0002042 Se0003077 "
    "Se0010014 Se0011049 Se0020067 Se0100070 Se0101065 Se0102026 Se0110068 "
    "Se0111028 Se0201040 Se1000041 Se1001062 Se1010064 Se1100004 Sf0000048 "
    "Sf0001067 Sf0010003 Sf0011064 Sf0020022 Sf0100017 Sf0101060 Sf0110077 "
    "Sf0200077 Sf1000057 Sf1010036 Sf1100005 Sh0100044 Si0000040 Si0001054 "
    "Si0002032 Si0003014 Si0010012 Si0011016 Si0020062 Si0100001 Si0101026 "
    "Si0102003 Si0110020 Si0200005 Si1000062 Si1001074 Si1010079 Si1100003 "
    "Sj0000004 Sj0001022 Sj0002001 Sj0003067 Sj0010002 Sj0011035 Sj0012074 "
    "Sj0020042 Sj0100007 Sj0101044 Sj0102027 Sj0110032 Sj0200033 Sj1000045 "
    "Sj1001017 Sj1010004 Sj1100073 Sk0000073 Sk0001075 Sk0002015 Sk0010033 "
    "Sk0011071 Sk0020047 Sk0100063 Sk0101072 Sk0102008 Sk0110080 Sk0200014 "
    "Sk1000021 Sk1010012 Sk1100046 Sl0000019 Sl0001046 Sl0002022 Sl0010001 "
    "Sl0011073 Sl0020042 Sl0100002 Sl0101028 Sl0110024 Sl0200006 Sl1000036 "
    "Sl1010048 Sl1100072 Sm0000020 Sn0100044 Sp0000006 Sp0001048 Sp0002028 "
    "Sp0010062 Sp0011067 Sp0020040 Sp0100062 Sp0101001 Sp0102019 Sp0110070 "
    "Sp0200065 Sp0210009 Sp1000016 Sp1001015 Sp1010070 Sp1100053 Sq0100010 "
    "Sr0000078 Sr0001047 Sr0010065 Sr0011060 Sr0020076 Sr0100037 Sr0101056 "
    "Sr0110061 Sr0200009 Sr0210039 Sr1000061 Su0100049 Sw0100044 Sx0000020 "
    "Ua0000077 Ua0010034 Ua0011042 Ua0020042 Ua0100066 Ua0101013 Ua0110077 "
    "Ua0200039 Ua1000042 Ua1010053 Ua1100013 Ub0000069 Ub0001080 Ub0010012 "
    "Ub0011069 Ub0020024 Ub0100028 Ub0101037 Ub0110067 Ub0200057 Ub1000051 "
    "Ub1010054 Ub1100018 Uc0000080 Uc0001024 Uc0002008 Uc0010037 Uc0011051 "
    "Uc0020045 Uc0021074 Uc0100037 Uc0101067 Uc0102007 Uc0200004 Uc0201051 "
    "Uc1000060 Uc1010044 Uc1100037 Ud0000061 Ud0001030 Ud0010077 Ud0011073 "
    "Ud0020035 Ud0100034 Ud0101066 Ud0200034 Ud1000049 Ud1010073 Ud1100075 "
    "Ue0000056 Ue0001020 Ue0010024 Ue0011080 Ue0020043 Ue0100032 Ue0101048 "
    "Ue0200066 Ue1100072 Uf0000044 Uf0001037 Uf0010040 Uf0011019 Uf0020031 "
    "Uf0100039 Uf0101048 Uf0200025 Uf1002029 Ug0201063 Ug1011024 Ug1020060 "
    "Ug2000019 Ug3000027 Uh0000038 Uh0002079 Uh0100045 Uh1002076 Ui1101067 "
    "Ui2000030 Ui3000018 Uj0002014 Uj0010009 Uj0100066 Uj0102079 Uj1002019 "
    "Uk1011064 Uk1101072 Uk2000036 Ul0000036 Ul0002056 Ul0030078 Ul0100080 "
    "Ul0102031 Ul1002024 Ul3000043 Um0201029 Um1101046 Um3000050 Un0000004 "
    "Un0010008 Uo1011043 Uo1101009 Uo2000034 Uo3000066 Up0000047 Up0002013 "
    "Up0010010 Up0100022 Up0102069 Up3000014 Uq1011046 Uq1101039 Uq2000005 "
    "Uq3000022 Ur0000005 Ur0002026 Ur0100050 Ut0000067 Ut0002078 Ut0010073 "
    "Uu1011069 Uu1101005 Uu2000067 Uu3000003 Uw0201070 Uw1011042 Uw1101037 "
    "Uw2000057 Uw3000031 Ux0000053 Ux0002028 Ux0010006 Ux0100022 Ux0102076 "
    "Ux1000018 Ux1001018 Ux1010018 Ux1011018 Ux1020018 Ux1100018 Ux1101018 "
    "Ux1110018 Ux1200018 Ux2000018 Ux2001018 Ux2010018 Ux2100018 Ea0000018 "
    "Ea0001018 Ea0002018 Ea0003018 Ea0010018 Ea0011018 Ea0012018 Ea0020018 "
    "Ea0021018 Ea0030018 Ea0100018 Ea0101018 Ea0102018 Ea0110018 Ea0111018 "
    "Ea0120018 Ea0200018 Ea0210018 Ea0300018 Ea1000018 Ea1001018 Ea1002018 "
    "Ea1010018 Ea1011050 Ea1100018 Ea1110018 Ea1200018 Ea2010018 Ea2100018 "
    "Eb0000033 Eb0001018 Eb0002079 Eb0003018 Eb0010063 Eb0011018 Eb0012018 "
    "Eb0020018 Eb0021018 Eb0100070 Eb0101018 Eb0110018 Eb0111018 Eb0120018 "
    "Eb0200018 Eb0201018 Eb0210018 Eb0300018 Eb1000018 Eb1001018 Eb1010018 "
    "Eb1011018 Eb1020018 Eb1100018 Eb1101018 Eb1110018 Eb1200018 Eb2000018 "
    "Eb2001018 Eb2010018 Eb2100018 Ec0000018 Ec0001018 Ec0002018 Ec0003018 "
    "Ec0010018 Ec0011018 Ec0012018 Ec0020018 Ec0021018 Ec0030018 Ec0100018 "
    "Ec0101018 Ec0102018 Ec0110018 Ec0111018 Ec0120018 Ec0200018 Ec0201012 "
    "Ec0210018 Ec0300018 Ec1000018 Ec1001018 Ec1002018 Ec1010018 Ec1011052 "
    "Ec1100018 Ec1101029 Ec1110018 Ec1200018 Ec2000069 Ec2010018 Ec2100018 "
    "Ec3000075 Ed0000048 Ed0001018 Ed0002075 Ed0003018 Ed0010035 Ed0011018 "
    "Ed0012018 Ed0020018 Ed0021018 Ed0100040 Ed0101018 Ed0110018 Ed0111018 "
    "Ed0120018 Ed0200018 Ed0201018 Ed0210018 Ed0300018 Ed1000018 Ed1001018 "
    "Ed1010018 Ed1011018 Ed1020018 Ed1100018 Ed1101018 Ed1110018 Ed1200018 "
    "Ed2000018 Ed2001018 Ed2010018 Ed2100018 Ed3000038 Ee0000018 Ee0001018 "
    "Ee0002018 Ee0003018 Ee0010018 Ee0011018 Ee0012018 Ee0020018 Ee0021018 "
    "Ee0030018 Ee0100018 Ee0101018 Ee0102018 Ee0110018 Ee0111018 Ee0120018 "
    "Ee0200018 Ee0210018 Ee0300018 Ee1000018 Ee1001018 Ee1002018 Ee1010018 "
    "Ee1100018 Ee1110018 Ee1200018 Ee2010018 Ee2100018 Ef0000018 Ef0001018 "
    "Ef0003018 Ef0010010 Ef0011018 Ef0012018 Ef0020018 Ef0021018 Ef0100074 "
    "Ef0101018 Ef0110018 Ef0111018 Ef0120018 Ef0200018 Ef0201018 Ef0210018 "
    "Ef0300018 Ef1000018 Ef1001018 Ef1010018 Ef1011018 Ef1020018 Ef1100018 "
    "Ef1101018 Ef1110018 Ef1200018 Ef2000018 Ef2001018 Ef2010018 Ef2100018 "
    "Eg0000018 Eg0001018 Eg0002018 Eg0003018 Eg0010018 Eg0011018 Eg0012018 "
    "Eg0020018 Eg0021018 Eg0030018 Eg0100018 Eg0101018 Eg0102018 Eg0110018 "
    "Eg0111018 Eg0120018 Eg0200018 Eg0210018 Eg0300018 Eg1000018 Eg1001018 "
    "Eg1002018 Eg1010018 Eg1100018 Eg1110018 Eg1200018 Eg2010018 Eg2100018 "
    "Eh0000004 Eh0001018 Eh0003018 Eh0010031 Eh0011018 Eh0012018 Eh0020018 "
    "Eh0021018 Eh0101018 Eh0110018 Eh0111018 Eh0120018 Eh0200018 Eh0201018 "
    "Eh0210018 Eh0300018 Eh1000018 Eh1001018 Eh1010018 Eh1011018 Eh1020018 "
    "Eh1100018 Eh1101018 Eh1110018 Eh1200018 Eh2000018 Eh2001018 Eh2010018 "
    "Eh2100018 Ei0000018 Ei0001018 Ei0002018 Ei0003018 Ei0010018 Ei0011018 "
    "Ei0012018 Ei0020018 Ei0021018 Ei0030018 Ei0100018 Ei0101018 Ei0102018 "
    "Ei0110018 Ei0111018 Ei0120018 Ei0200018 Ei0201027 Ei0210018 Ei0300018 "
    "Ei1000018 Ei1001018 Ei1002018 Ei1010018 Ei1011036 Ei1100018 Ei1101066 "
    "Ei1110018 Ei1200018 Ei2000016 Ei2010018 Ei2100018 Ei3000042 Ej0000077 "
    "Ej0001018 Ej0002020 Ej0003018 Ej0010068 Ej0011018 Ej0012018 Ej0020018 "
    "Ej0021018 Ej0100069 Ej0101018 Ej0102032 Ej0110018 Ej0111018 Ej0120018 "
    "Ej0200018 Ej0201018 Ej0210018 Ej0300018 Ej1000018 Ej1001018 Ej1010018 "
    "Ej1011018 Ej1020018 Ej1100018 Ej1101018 Ej1110018 Ej1200018 Ej2000018 "
    "Ej2001018 Ej2010018 Ej2100018 Ek0000018 Ek0001018 Ek0002018 Ek0003018 "
    "Ek0010018 Ek0011018 Ek0012018 Ek0020018 Ek0021018 Ek0030018 Ek0100018 "
    "Ek0101018 Ek0102018 Ek0110018 Ek0111018 Ek0120018 Ek0200018 Ek0210018 "
    "Ek0300018 Ek1000018 Ek1001018 Ek1002018 Ek1010018 Ek1011068 Ek1100018 "
    "Ek1110018 Ek1200018 Ek2000068 Ek2010018 Ek2100018 Ek3000057 El0000003 "
    "El0001018 El0002041 El0003018 El0010051 El0011018 El0012018 El0020018 "
    "El0021018 El0101018 El0102030 El0110018 El0111018 El0120018 El0200018 "
    "El0201018 El0210018 El0300018 El1000018 El1001018 El1010018 El1011018 "
    "El1020018 El1100018 El1101018 El1110018 El1200018 El2000018 El2001018 "
    "El2010018 El2100018 Em0000018 Em0001018 Em0002018 Em0003018 Em0010018 "
    "Em0011018 Em0012018 Em0020018 Em0021018 Em0030018 Em0100018 Em0101018 "
    "Em0102018 Em0110018 Em0111018 Em0120018 Em0200018 Em0201046 Em0210018 "
    "Em0300018 Em1000018 Em1001018 Em1002018 Em1010018 Em1011006 Em1100018 "
    "Em1101051 Em1110018 Em1200018 Em2000028 Em2010018 Em2100018 En0000056 "
    "En0001018 En0002068 En0003018 En0010049 En0011018 En0012018 En0020018 "
    "En0021018 En0100075 En0101018 En0102034 En0110018 En0111018 En0120018 "
    "En0200018 En0201018 En0210018 En0300018 En1000018 En1001018 En1010018 "
    "En1011018 En1020018 En1100018 En1101018 En1110018 En1200018 En2000018 "
    "En2001018 En2010018 En2100018 En3000048 Eo0000018 Eo0001018 Eo0002018 "
    "Eo0003018 Eo0010018 Eo0011018 Eo0012018 Eo0020018 Eo0021018 Eo0030018 "
    "Eo0100018 Eo0101018 Eo0102018 Eo0110018 Eo0111018 Eo0120018 Eo0200018 "
    "Eo0201043 Eo0210018 Eo0300018 Eo1000018 Eo1001018 Eo1002018 Eo1010018 "
    "Eo1011010 Eo1100018 Eo1101077 Eo1110018 Eo1200018 Eo2000069 Eo2010018 "
    "Eo2100018 Eo3000080 Ep0000010 Ep0001018 Ep0002021 Ep0003018 Ep0010080 "
    "Ep0011018 Ep0012018 Ep0020018 Ep0021018 Ep0100034 Ep0101018 Ep0102004 "
    "Ep0110018 Ep0111018 Ep0120018 Ep0200018 Ep0201018 Ep0210018 Ep0300018 "
    "Ep1000018 Ep1001018 Ep1010018 Ep1011018 Ep1020018 Ep1100018 Ep1101018 "
    "Ep1110018 Ep1200018 Ep2000018 Ep2001018 Ep2010018 Ep2100018 Ep3000064 "
    "Eq0000018 Eq0001018 Eq0002018 Eq0003018 Eq0010018 Eq0011018 Eq0012018 "
    "Eq0020018 Eq0021018 Eq0030018 Eq0100018 Eq0101018 Eq0102018 Eq0110018 "
    "Eq0111018 Eq0120018 Eq0200018 Eq0210018 Eq0300018 Eq1000018 Eq1001018 "
    "Eq1002018 Eq1010018 Eq1100018 Eq1110018 Eq1200018 Eq2000003 Eq2010018 "
    "Eq2100018 Er0000033 Er0001018 Er0002024 Er0003018 Er0010073 Er0011018 "
    "Er0012018 Er0020018 Er0021018 Er0100067 Er0101018 Er0110018 Er0111018 "
    "Er0120018 Er0200018 Er0201018 Er0210018 Er0300018 Er1000018 Er1001018 "
    "Er1010018 Er1011018 Er1020018 Er1100018 Er1101018 Er1110018 Er1200018 "
    "Er2000018 Er2001018 Er2010018 Er2100018 Es0000018 Es0001018 Es0002018 "
    "Es0003018 Es0010018 Es0011018 Es0012018 Es0020018 Es0021018 Es0030018 "
    "Es0100018 Es0101018 Es0102018 Es0110018 Es0111018 Es0120018 Es0200018 "
    "Es0210018 Es0300018 Es1000018 Es1001018 Es1002018 Es1010018 Es1100018 "
    "Es1110018 Es1200018 Es2010018 Es2100018 Et0000039 Et0001018 Et0003018 "
    "Et0010055 Et0011018 Et0012018 Et0020063 Et0021018 Et0100062 Et0101018 "
    "Et0110018 Et0111018 Et0120018 Et0200018 Et0201018 Et0210018 Et0300018 "
    "Et1000018 Et1001018 Et1010018 Et1011018 Et1020018 Et1100018 Et1101018 "
    "Et1110018 Et1200018 Et2000018 Et2001018 Et2010018 Et2100018 Eu0000018 "
    "Eu0001018 Eu0002018 Eu0003018 Eu0010018 Eu0011018 Eu0012018 Eu0020018 "
    "Eu0021018 Eu0030018 Eu0100018 Eu0101018 Eu0102018 Eu0110018 Eu0111018 "
    "Eu0120018 Eu0200018 Eu0201031 Eu0210018 Eu0300018 Eu1000018 Eu1001018 "
    "Eu1002018 Eu1010018 Eu1011007 Eu1100018 Eu1101058 Eu1110018 Eu1200018 "
    "Eu2000008 Eu2001022 Eu2010018 Eu2100018 Eu3000023 Ev0000043 Ev0001018 "
    "Ev0002070 Ev0003018 Ev0010010 Ev0011018 Ev0012018 Ev0020018 Ev0021018 "
    "Ev0100069 Ev0101018 Ev0102001 Ev0110018 Ev0111018 Ev0120018 Ev0200018 "
    "Ev0201018 Ev0210018 Ev0300018 Ev1000018 Ev1001018 Ev1002040 Ev1010018 "
    "Ev1011018 Ev1020018 Ev1100018 Ev1101018 Ev1110018 Ev1200018 Ev2000018 "
    "Ev2001018 Ev2010018 Ev2100018 Ev3000046 Ew0000018 Ew0001018 Ew0002018 "
    "Ew0003018 Ew0010041 Ew0011041 Ew0012041 Ew0020041 Ew0021041 Ew0030041 "
    "Ew0100041 Ew0101041 Ew0102041 Ew0110041 Ew0111041 Ew0120041 Ew0200012 "
    "Ew0210012 Ew0300012 Ew1000060 Ew1001060 Ew1002060 Ew1010022 Ew1100003 "
    "Ew1110003 Ew1200003 Ew2010003 Ew2100003 Ex0000038 Ex0001003 Ex0002068 "
    "Ex0003003 Ex0010076 Ex0011003 Ex0012003 Ex0020003 Ex0021003 Ex0100070 "
    "Ex0101003 Ex0102053 Ex0110003 Ex0111003 Ex0120003 Ex0200003 Ex0201003 "
    "Ex0210003 Ex0300003 Ex1000003 Ex1001003 Ex1010003 Ex1011003 Ex1020003 "
    "Ex1100003 Ex1101003 Ex1110003 Ex1200003 Ex2000003 Ex2001003 Ex2010003 "
    "Ex2100003 Ex3000068 "
)

CERT_L11_R1 = (
    "Sa0000033 Sa0001037 Sa0002042 Sa0003071 Sa0010017 Sa0011078 Sa0012046 "
    "Sa0020056 Sa0100017 Sa0101064 Sa0102021 Sa0110043 Sa0200027 Sa1000039 "
    "Sa1001070 Sa1010012 Sa1100036 Sb0000034 Sb0001024 Sb0002052 Sb0003067 "
    "Sb0010020 Sb0011035 Sb0020059 Sb0100025 Sb0101038 Sb0102040 Sb0110072 "
    "Sb0200079 Sb0201005 Sb1000033 Sb1001075 Sb1010061 Sb1100068 Sc0000072 "
    "Sc0001064 Sc0002063 Sc0003048 Sc0010075 Sc0011073 Sc0020044 Sc0100076 "
    "Sc0101044 Sc0102012 Sc0110078 Sc0200074 Sc1000036 Sc1001014 Sc1010064 "
    "Sc1100008 Sd0000064 Sd0001049 Sd0002037 Sd0003048 Sd0010045 Sd0011008 "
    "Sd0012068 Sd0020019 Sd0100044 Sd0101058 Sd0102048 Sd0110072 Sd0200003 "
    "Sd1000065 Sd1001074 Sd1010010 Sd1100043 Se0000055 Se0001026 Se0002023 "
    "Se0003077 Se0010074 Se0011028 Se0020037 Se0100028 Se0101038 Se0102078 "
    "Se0110011 Se0200046 Se0201029 Se1000047 Se1001033 Se1010052 Se1100079 "
    "Sf0000006 Sf0001040 Sf0010039 Sf0011061 Sf0020025 Sf0100029 Sf0101063 "
    "Sf0200048 Sf1000045 Sf1010054 Sf1100062 Si0000053 Si0001002 Si0002042 "
    "Si0003038 Si0010021 Si0011004 Si0012041 Si0020020 Si0100029 Si0101027 "
    "Si0102034 Si0110038 Si0200009 Si1000047 Si1001055 Si1010001 Si1100046 "
    "Sj0000072 Sj0001067 Sj0002066 Sj0003077 Sj0010040 Sj0011067 Sj0012020 "
    "Sj0020029 Sj0100033 Sj0101028 Sj0102011 Sj0110004 Sj0200036 Sj1000063 "
    "Sj1001005 Sj1010031 Sj1100039 Sk0000076 Sk0001018 Sk0002072 Sk0010015 "
    "Sk0011071 Sk0020077 Sk0101069 Sk0110011 Sk0200003 Sk1000036 Sk1010057 "
    "Sk1100079 Sl0000031 Sl0001025 Sl0002057 Sl0010076 Sl0011048 Sl0020041 "
    "Sl0100029 Sl0101045 Sl0110014 Sl0200015 Sl1000054 Sl1010024 Sl1100012 "
    "Sm0000011 Sn0100028 Sp0000026 Sp0001054 Sp0002071 Sp0010057 Sp0011028 "
    "Sp0020064 Sp0100007 Sp0101016 Sp0110069 Sp0200078 Sp1000037 Sp1001080 "
    "Sp1010049 Sp1100008 Sp1101074 Sq0100047 Sr0000049 Sr0001080 Sr0010026 "
    "Sr0011074 Sr0020001 Sr0100026 Sr0101078 Sr0110033 Sr0200048 Sr0201055 "
    "Sr1000056 Sr1101079 Su0100073 Sw0100046 Sx0000053 Ua0000029 Ua0010032 "
    "Ua0011003 Ua0020028 Ua0100060 Ua0101080 Ua0110076 Ua0200003 Ua1000078 "
    "Ua1010080 Ua1100052 Ub0000080 Ub0001003 Ub0010075 Ub0011055 Ub0020007 "
    "Ub0100007 Ub0101053 Ub0110056 Ub0200057 Ub1000060 Ub1010036 Ub1100030 "
    "Uc0000015 Uc0001080 Uc0002006 Uc0010031 Uc0011046 Uc0020070 Uc0100050 "
    "Uc0101013 Uc0102078 Uc0110056 Uc0200061 Uc0201029 Uc1000021 Uc1010026 "
    "Uc1100031 Uc1101078 Ud0000025 Ud0001054 Ud0010044 Ud0011052 Ud0020062 "
    "Ud0100049 Ud0101003 Ud0200057 Ud1000010 Ud1010031 Ue0000041 Ue0001014 "
    "Ue0010003 Ue0011014 Ue0020058 Ue0100020 Ue0101069 Ue0200014 Ue1101002 "
    "Uf0000035 Uf0001064 Uf0002021 Uf0010025 Uf0011040 Uf0020061 Uf0030030 "
    "Uf0100012 Uf0101075 Uf0200030 Uf1002028 Ug0201075 Ug1020024 Ug1101046 "
    "Ug2000005 Ug2001075 Ug3000019 Uh0002010 Uh0100060 Uh0102002 Ui1101032 "
    "Ui2000077 Ui3000011 Uj0002037 Uj0100039 Uj0102067 Uj1002021 Uk1011053 "
    "Uk1101067 Uk2000003 Uk3000046 Ul0000070 Ul0002039 Ul0100042 Ul0102036 "
    "Ul1002025 Um0201031 Um1101019 Un0000069 Un0002066 Un0010002 Uo1011063 "
    "Uo1101029 Uo2000068 Uo3000042 Up0000056 Up0002007 Up0010040 Up0100037 "
    "Uq1011049 Uq1101042 Uq2000058 Uq3000001 Ur0000062 Ur0002019 Ur0010010 "
    "Ur0100012 Us2000059 Ut0000076 Ut0002079 Ut0010069 Uu1011062 Uu1101020 "
    "Uu2000008 Uu3000033 Uw0201062 Uw1011034 Uw1101069 Uw2000079 Uw3000061 "
    "Ux0000079 Ux0002056 Ux0010074 Ux0100020 Ux0102055 Ux0200008 Ux0201008 "
    "Ux0210008 Ux0300008 Ux1000078 Ux1001078 Ux1010057 Ux1011057 Ux1020057 "
    "Ux1100057 Ux1101057 Ux1110057 Ux1200057 Ux2000057 Ux2001057 Ux2010057 "
    "Ux2100057 Ea0000057 Ea0001057 Ea0002057 Ea0003057 Ea0010057 Ea0011057 "
    "Ea0012057 Ea0020057 Ea0021057 Ea0030057 Ea0100057 Ea0101057 Ea0102057 "
    "Ea0110057 Ea0111057 Ea0120057 Ea0200057 Ea0210057 Ea0300057 Ea1000057 "
    "Ea1001057 Ea1002057 Ea1010057 Ea1011039 Ea1100057 Ea1101074 Ea1110057 "
    "Ea1200057 Ea2010057 Ea2100057 Eb0000015 Eb0001057 Eb0002054 Eb0003057 "
    "Eb0010027 Eb0011057 Eb0012057 Eb0020057 Eb0021057 Eb0100076 Eb0101057 "
    "Eb0110057 Eb0111057 Eb0120057 Eb0200057 Eb0201057 Eb0210057 Eb0300057 "
    "Eb1000057 Eb1001057 Eb1010057 Eb1011057 Eb1020057 Eb1100057 Eb1101057 "
    "Eb1110057 Eb1200057 Eb2000057 Eb2001057 Eb2010057 Eb2100057 Ec0000057 "
    "Ec0001057 Ec0002057 Ec0003057 Ec0010057 Ec0011057 Ec0012057 Ec0020057 "
    "Ec0021057 Ec0030057 Ec0100057 Ec0101057 Ec0102057 Ec0110057 Ec0111057 "
    "Ec0120057 Ec0200057 Ec0201003 Ec0210057 Ec0300057 Ec1000057 Ec1001057 "
    "Ec1002057 Ec1010057 Ec1011054 Ec1100057 Ec1101064 Ec1110057 Ec1200057 "
    "Ec2000048 Ec2010057 Ec2100057 Ed0000075 Ed0001057 Ed0002018 Ed0003057 "
    "Ed0010005 Ed0011057 Ed0012057 Ed0020057 Ed0021057 Ed0100079 Ed0101057 "
    "Ed0102079 Ed0110057 Ed0111057 Ed0120057 Ed0200057 Ed0201057 Ed0210057 "
    "Ed0300057 Ed1000057 Ed1001057 Ed1010057 Ed1011057 Ed1020057 Ed1100057 "
    "Ed1101057 Ed1110057 Ed1200057 Ed2000057 Ed2001057 Ed2010057 Ed2100057 "
    "Ee0000057 Ee0001057 Ee0002057 Ee0003057 Ee0010057 Ee0011057 Ee0012057 "
    "Ee0020057 Ee0021057 Ee0030057 Ee0100057 Ee0101057 Ee0102057 Ee0110057 "
    "Ee0111057 Ee0120057 Ee0200057 Ee0210057 Ee0300057 Ee1000057 Ee1001057 "
    "Ee1002057 Ee1010057 Ee1100057 Ee1110057 Ee1200057 Ee2010057 Ee2100057 "
    "Ef0000024 Ef0001057 Ef0003057 Ef0010013 Ef0011057 Ef0012057 Ef0020057 "
    "Ef0021057 Ef0100068 Ef0101057 Ef0110057 Ef0111057 Ef0120057 Ef0200057 "
    "Ef0201057 Ef0210057 Ef0300057 Ef1000057 Ef1001057 Ef1010057 Ef1011057 "
    "Ef1020057 Ef1100057 Ef1101057 Ef1110057 Ef1200057 Ef2000057 Ef2001057 "
    "Ef2010057 Ef2100057 Eg0000057 Eg0001057 Eg0002057 Eg0003057 Eg0010057 "
    "Eg0011057 Eg0012057 Eg0020057 Eg0021057 Eg0030057 Eg0100057 Eg0101057 "
    "Eg0102057 Eg0110057 Eg0111057 Eg0120057 Eg0200057 Eg0210057 Eg0300057 "
    "Eg1000057 Eg1001057 Eg1002057 Eg1010057 Eg1100057 Eg1110057 Eg1200057 "
    "Eg2010057 Eg2100057 Eh0000037 Eh0001057 Eh0003057 Eh0010034 Eh0011057 "
    "Eh0012057 Eh0020057 Eh0021057 Eh0100075 Eh0101057 Eh0110057 Eh0111057 "
    "Eh0120057 Eh0200057 Eh0201057 Eh0210057 Eh0300057 Eh1000057 Eh1001057 "
    "Eh1010057 Eh1011057 Eh1020057 Eh1100057 Eh1101057 Eh1110057 Eh1200057 "
    "Eh2000057 Eh2001057 Eh2010057 Eh2100057 Ei0000057 Ei0001057 Ei0002057 "
    "Ei0003057 Ei0010057 Ei0011057 Ei0012057 Ei0020057 Ei0021057 Ei0030057 "
    "Ei0100057 Ei0101057 Ei0102057 Ei0110057 Ei0111057 Ei0120057 Ei0200057 "
    "Ei0201041 Ei0210057 Ei0300057 Ei1000057 Ei1001057 Ei1002057 Ei1010057 "
    "Ei1011012 Ei1100057 Ei1101028 Ei1110057 Ei1200057 Ei2000054 Ei2010057 "
    "Ei2100057 Ei3000032 Ej0000036 Ej0001057 Ej0002037 Ej0003057 Ej0010009 "
    "Ej0011057 Ej0012057 Ej0020057 Ej0021057 Ej0100071 Ej0101057 Ej0102062 "
    "Ej0110057 Ej0111057 Ej0120057 Ej0200057 Ej0201057 Ej0210057 Ej0300057 "
    "Ej1000057 Ej1001057 Ej1002061 Ej1010057 Ej1011057 Ej1020057 Ej1100057 "
    "Ej1101057 Ej1110057 Ej1200057 Ej2000057 Ej2001057 Ej2010057 Ej2100057 "
    "Ek0000057 Ek0001057 Ek0002057 Ek0003057 Ek0010057 Ek0011057 Ek0012057 "
    "Ek0020057 Ek0021057 Ek0030057 Ek0100057 Ek0101057 Ek0102057 Ek0110057 "
    "Ek0111057 Ek0120057 Ek0200057 Ek0210057 Ek0300057 Ek1000057 Ek1001057 "
    "Ek1002057 Ek1010057 Ek1100057 Ek1101023 Ek1110057 Ek1200057 Ek2000018 "
    "Ek2010057 Ek2100057 Ek3000067 El0000005 El0001057 El0002066 El0003057 "
    "El0010044 El0011057 El0012057 El0020057 El0021057 El0100067 El0101057 "
    "El0102061 El0110057 El0111057 El0120057 El0200057 El0201057 El0210057 "
    "El0300057 El1000057 El1001057 El1010057 El1011057 El1020057 El1100057 "
    "El1101057 El1110057 El1200057 El2000057 El2001057 El2010057 El2100057 "
    "Em0000057 Em0001057 Em0002057 Em0003057 Em0010057 Em0011057 Em0012057 "
    "Em0020057 Em0021057 Em0030057 Em0100057 Em0101057 Em0102057 Em0110057 "
    "Em0111057 Em0120057 Em0200057 Em0201063 Em0210057 Em0300057 Em1000057 "
    "Em1001057 Em1002057 Em1010057 Em1100057 Em1101046 Em1110057 Em1200057 "
    "Em2000019 Em2010057 Em2100057 En0000077 En0001057 En0002022 En0003057 "
    "En0010079 En0011057 En0012057 En0020057 En0021057 En0100027 En0101057 "
    "En0102052 En0110057 En0111057 En0120057 En0200057 En0201057 En0210057 "
    "En0300057 En1000057 En1001057 En1002058 En1010057 En1011057 En1020057 "
    "En1100057 En1101057 En1110057 En1200057 En2000057 En2001057 En2010057 "
    "En2100057 En3000019 Eo0000057 Eo0001057 Eo0002057 Eo0003057 Eo0010057 "
    "Eo0011057 Eo0012057 Eo0020057 Eo0021057 Eo0030057 Eo0100057 Eo0101057 "
    "Eo0102057 Eo0110057 Eo0111057 Eo0120057 Eo0200057 Eo0201057 Eo0210057 "
    "Eo0300057 Eo1000057 Eo1001057 Eo1002057 Eo1010057 Eo1011014 Eo1100057 "
    "Eo1101007 Eo1110057 Eo1200057 Eo2000041 Eo2010057 Eo2100057 Eo3000044 "
    "Ep0000062 Ep0001057 Ep0002002 Ep0003057 Ep0010040 Ep0011057 Ep0012057 "
    "Ep0020057 Ep0021057 Ep0100002 Ep0101057 Ep0102022 Ep0110057 Ep0111057 "
    "Ep0120057 Ep0200057 Ep0201057 Ep0210057 Ep0300057 Ep1000057 Ep1001057 "
    "Ep1002077 Ep1010057 Ep1011057 Ep1020057 Ep1100057 Ep1101057 Ep1110057 "
    "Ep1200057 Ep2000057 Ep2001057 Ep2010057 Ep2100057 Ep3000040 Eq0000057 "
    "Eq0001057 Eq0002057 Eq0003057 Eq0010057 Eq0011057 Eq0012057 Eq0020057 "
    "Eq0021057 Eq0030057 Eq0100057 Eq0101057 Eq0102057 Eq0110057 Eq0111057 "
    "Eq0120057 Eq0200057 Eq0210057 Eq0300057 Eq1000057 Eq1001057 Eq1002057 "
    "Eq1010057 Eq1100057 Eq1110057 Eq1200057 Eq2000009 Eq2010057 Eq2100057 "
    "Er0000054 Er0001057 Er0002002 Er0003057 Er0010064 Er0011057 Er0012057 "
    "Er0020057 Er0021057 Er0100076 Er0101057 Er0110057 Er0111057 Er0120057 "
    "Er0200057 Er0201057 Er0210057 Er0300057 Er1000057 Er1001057 Er1010057 "
    "Er1011057 Er1020057 Er1100057 Er1101057 Er1110057 Er1200057 Er2000057 "
    "Er2001057 Er2010057 Er2100057 Es0000057 Es0001057 Es0002057 Es0003057 "
    "Es0010057 Es0011057 Es0012057 Es0020057 Es0021057 Es0030057 Es0100057 "
    "Es0101057 Es0102057 Es0110057 Es0111057 Es0120057 Es0200057 Es0210057 "
    "Es0300057 Es1000057 Es1001057 Es1002057 Es1010057 Es1100057 Es1110057 "
    "Es1200057 Es2010057 Es2100057 Et0000036 Et0001057 Et0003057 Et0010013 "
    "Et0011045 Et0012045 Et0020075 Et0021051 Et0100011 Et0101051 Et0110051 "
    "Et0111051 Et0120051 Et0200051 Et0201051 Et0210051 Et0300051 Et1000051 "
    "Et1001051 Et1010051 Et1011051 Et1020051 Et1100051 Et1101051 Et1110051 "
    "Et1200051 Et2000051 Et2001051 Et2010051 Et2100051 Eu0000051 Eu0001051 "
    "Eu0002051 Eu0003051 Eu0010051 Eu0011051 Eu0012051 Eu0020051 Eu0021051 "
    "Eu0030051 Eu0100051 Eu0101051 Eu0102051 Eu0110051 Eu0111051 Eu0120051 "
    "Eu0200051 Eu0201039 Eu0210051 Eu0300051 Eu1000051 Eu1001051 Eu1002051 "
    "Eu1010051 Eu1011029 Eu1100051 Eu1101028 Eu1110051 Eu1200051 Eu2000021 "
    "Eu2001042 Eu2010051 Eu2100051 Eu3000010 Ev0000050 Ev0001051 Ev0002056 "
    "Ev0003051 Ev0011051 Ev0012051 Ev0020051 Ev0021051 Ev0100010 Ev0101051 "
    "Ev0102002 Ev0110051 Ev0111051 Ev0120051 Ev0200051 Ev0201051 Ev0210051 "
    "Ev0300051 Ev1000051 Ev1001051 Ev1002012 Ev1010051 Ev1011051 Ev1020051 "
    "Ev1100051 Ev1101051 Ev1110051 Ev1200051 Ev2000051 Ev2001051 Ev2010051 "
    "Ev2100051 Ev3000001 Ew0000051 Ew0001051 Ew0002051 Ew0003051 Ew0010023 "
    "Ew0011023 Ew0012023 Ew0020023 Ew0021023 Ew0030023 Ew0100023 Ew0101023 "
    "Ew0102023 Ew0110023 Ew0111023 Ew0120023 Ew0200018 Ew0210018 Ew0300018 "
    "Ew1000075 Ew1001024 Ew1002024 Ew1010007 Ew1100051 Ew1110051 Ew1200051 "
    "Ew2010051 Ew2100051 Ex0000024 Ex0001051 Ex0002019 Ex0003051 Ex0010077 "
    "Ex0011051 Ex0012051 Ex0020051 Ex0021051 Ex0100042 Ex0101051 Ex0102009 "
    "Ex0110051 Ex0111051 Ex0120051 Ex0200051 Ex0201051 Ex0210051 Ex0300051 "
    "Ex1000051 Ex1001051 Ex1002047 Ex1010051 Ex1011051 Ex1020051 Ex1100051 "
    "Ex1101051 Ex1110051 Ex1200051 Ex2000051 Ex2001051 Ex2010051 Ex2100051 "
    "Ex3000036 "
)

CERT_L11_R2 = (
    "Sa0000069 Sa0001065 Sa0002006 Sa0003032 Sa0010047 Sa0011007 Sa0020066 "
    "Sa0100078 Sa0101055 Sa0102037 Sa0110020 Sa0200057 Sa1000059 Sa1001065 "
    "Sa1010064 Sa1100066 Sb0000024 Sb0001061 Sb0002072 Sb0003017 Sb0010068 "
    "Sb0011026 Sb0012035 Sb0020045 Sb0100036 Sb0101004 Sb0102023 Sb0110067 "
    "Sb0200002 Sb0201051 Sb1000017 Sb1001031 Sb1010052 Sb1100066 Sc0000076 "
    "Sc0001035 Sc0002042 Sc0003025 Sc0010050 Sc0011017 Sc0012064 Sc0020062 "
    "Sc0100008 Sc0101030 Sc0102046 Sc0110055 Sc0120079 Sc0200055 Sc0210049 "
    "Sc1000011 Sc1001009 Sc1010046 Sc1100003 Sd0000074 Sd0002049 Sd0003010 "
    "Sd0010064 Sd0011051 Sd0012003 Sd0020044 Sd0100039 Sd0101057 Sd0102016 "
    "Sd0110057 Sd0111028 Sd0200011 Sd1000016 Sd1001075 Sd1010042 Sd1100079 "
    "Se0000072 Se0001077 Se0002076 Se0003005 Se0010049 Se0011043 Se0012005 "
    "Se0020038 Se0100039 Se0101040 Se0102036 Se0110067 Se0120009 Se0200045 "
    "Se0201016 Se1000032 Se1001069 Se1010007 Se1100062 Sf0000014 Sf0001004 "
    "Sf0002001 Sf0010012 Sf0011019 Sf0020025 Sf0100035 Sf0110066 Sf1000066 "
    "Sf1010024 Sf1100042 Sg0100017 Sh0100009 Si0000029 Si0001021 Si0002071 "
    "Si0003080 Si0010052 Si0011037 Si0012078 Si0020027 Si0100033 Si0101005 "
    "Si0102030 Si0110048 Si0111044 Si0200072 Si1000069 Si1001038 Si1010013 "
    "Si1100078 Sj0000069 Sj0001051 Sj0002005 Sj0003027 Sj0010033 Sj0011057 "
    "Sj0012033 Sj0020036 Sj0100059 Sj0101076 Sj0102028 Sj0110053 Sj0111080 "
    "Sj0200048 Sj1000014 Sj1001054 Sj1010046 Sj1100076 Sk0000028 Sk0001072 "
    "Sk0002015 Sk0003055 Sk0010035 Sk0011008 Sk0020067 Sk0100068 Sk0102054 "
    "Sk0110065 Sk0200029 Sk1000022 Sk1001048 Sk1100073 Sl0000072 Sl0001014 "
    "Sl0002017 Sl0003046 Sl0010067 Sl0011032 Sl0020058 Sl0100072 Sl0102045 "
    "Sl0110054 Sl0200045 Sl1000062 Sl1001033 Sl1010033 Sl1100027 Sm0000066 "
    "Sn0100069 Sp0000035 Sp0001062 Sp0002038 Sp0003066 Sp0010059 Sp0011075 "
    "Sp0020043 Sp0100025 Sp0101060 Sp0102072 Sp0110038 Sp0200037 Sp0210058 "
    "Sp1000007 Sp1010018 Sp1100057 Sq0100028 Sr0000024 Sr0100004 Sr0110018 "
    "Sr1000030 Sr1100061 Ss0000067 St0000068 Su0100070 Sv0000024 Sw0100037 "
    "Sx0000034 Ua0000039 Ua0001003 Ua0002055 Ua0010057 Ua0100054 Ua0101039 "
    "Ua0110073 Ua1000004 Ua1010047 Ua1100051 Ub0000021 Ub0001007 Ub0002072 "
    "Ub0010060 Ub0020070 Ub0021031 Ub0100021 Ub1000016 Ub1010017 Ub1100015 "
    "Uc0000054 Uc0001059 Uc0002039 Uc0003070 Uc0010049 Uc0011025 Uc0020019 "
    "Uc0100024 Uc0101050 Uc0102010 Uc0110033 Uc0200003 Uc1000076 Uc1001008 "
    "Uc1010035 Uc1100051 Uc2000033 Ud0000075 Ud0001041 Ud0010006 Ud0011003 "
    "Ud0100002 Ud1000020 Ud1001043 Ud1002029 Ud1010029 Ud1100007 Ue0000035 "
    "Ue0001077 Ue0010007 Ue0011056 Ue0100059 Ue0101057 Ue0110026 Ue1000068 "
    "Ue1100049 Uf0000076 Uf0010077 Uf0011055 Uf0100050 Uf0110020 Uf1000019 "
    "Uf1002025 Uf1100020 Ug0101013 Uh0010077 Uh0020053 Uh0100063 Uh0101003 "
    "Uh0200039 Uh1001044 Uh1002080 Ui0101069 Ui1200032 Uj0001029 Uj0100075 "
    "Uj1002050 Uk0000022 Uk0100077 Uk0101031 Uk1000038 Uk1200075 Ul0001080 "
    "Ul0010070 Ul0101002 Ul1000010 Ul1001075 Ul1002027 Ul3000029 Um1200003 "
    "Un0001047 Un3000047 Uo0101002 Uo1200074 Up0001069 Up0002013 Up0010065 "
    "Up0020016 Up0101041 Up0102007 Up0111038 Up0200031 Up1001066 Uq0101047 "
    "Ur0001070 Ur0010024 Ur0101076 Ut0010079 Ut0020059 Ut0101010 Ut0111011 "
    "Ut0200077 Ut1001036 Ut3000066 Uu0101042 Uv0001005 Uv0102045 Uw1200025 "
    "Ux0001025 Ux0002041 Ux0010030 Ux0020010 Ux0101031 Ux0111065 Ux0200038 "
    "Ux1001024 Ux3000050 Eb0001040 Eb0010059 Eb0020027 Eb0111035 Eb0200022 "
    "Eb1001077 Ec1200026 Ed0001065 Ed0002013 Ed0010045 Ed0020046 Ed0101076 "
    "Ed0102070 Ed0200070 Ed1001066 Ed3000028 Ee0101009 Ef0010003 Eh0010053 "
    "Ej0001043 Ej0002075 Ej0010011 Ej0020067 Ej0101014 Ej0200028 Ej1001018 "
    "Ej3000067 Ek0101020 El0001034 El0010001 El0020008 El0100045 El0101060 "
    "El0102039 El0110045 El0111018 El0120045 El0200012 El0201045 El0210045 "
    "El0300045 El1000045 El1001063 El1010045 El1020045 El1100045 El1101045 "
    "El1110045 El1200045 El2000045 El2001045 El2010045 El2100045 El3000048 "
    "Em0000045 Em0001045 Em0002045 Em0003045 Em0010045 Em0011045 Em0012045 "
    "Em0020045 Em0021045 Em0030045 Em0100045 Em0102045 Em0110045 Em0111045 "
    "Em0120045 Em0200045 Em0201045 Em0210045 Em0300045 Em1000045 Em1001045 "
    "Em1002045 Em1010045 Em1011045 Em1020045 Em1100045 Em1101045 Em1110045 "
    "Em1200042 Em2000045 Em2001045 Em2010045 Em2100045 Em3000045 En0000057 "
    "En0001056 En0002076 En0003057 En0011057 En0012057 En0020020 En0030057 "
    "En0100057 En0101032 En0102062 En0110057 En0111019 En0120057 En0200010 "
    "En0201057 En0210057 En0300057 En1000057 En1001074 En1010057 En1020057 "
    "En1100057 En1101057 En1110057 En1200057 En2000057 En2001057 En2010057 "
    "En2100057 En3000055 Eo0000057 Eo0001057 Eo0002057 Eo0003057 Eo0010057 "
    "Eo0011057 Eo0012057 Eo0020057 Eo0021057 Eo0030057 Eo0100057 Eo0101046 "
    "Eo0102057 Eo0110057 Eo0111057 Eo0120057 Eo0200057 Eo0201057 Eo0210057 "
    "Eo0300057 Eo1000057 Eo1001057 Eo1002057 Eo1010057 Eo1011057 Eo1020057 "
    "Eo1100057 Eo1101057 Eo1110057 Eo1200010 Eo2000057 Eo2001057 Eo2010057 "
    "Eo2100057 Eo3000057 Ep0000057 Ep0001008 Ep0002050 Ep0003057 Ep0010037 "
    "Ep0011057 Ep0012057 Ep0020072 Ep0030057 Ep0100057 Ep0101068 Ep0102025 "
    "Ep0110057 Ep0111066 Ep0120057 Ep0200056 Ep0201057 Ep0210057 Ep0300057 "
    "Ep1000057 Ep1001075 Ep1002054 Ep1010057 Ep1020057 Ep1100057 Ep1101057 "
    "Ep1110057 Ep1200057 Ep2000057 Ep2001057 Ep2010057 Ep2100057 Ep3000002 "
    "Eq0000057 Eq0001057 Eq0002057 Eq0003057 Eq0010057 Eq0011057 Eq0012057 "
    "Eq0020057 Eq0021057 Eq0030057 Eq0100057 Eq0101057 Eq0102057 Eq0110057 "
    "Eq0111057 Eq0120057 Eq0200057 Eq0201057 Eq0210057 Eq0300057 Eq1000057 "
    "Eq1001057 Eq1002057 Eq1010057 Eq1011057 Eq1020057 Eq1100057 Eq1101057 "
    "Eq1110057 Eq2000057 Eq2001057 Eq2010057 Eq2100057 Eq3000057 Er0000057 "
    "Er0001034 Er0003057 Er0010034 Er0011057 Er0012057 Er0020054 Er0030057 "
    "Er0100029 Er0110029 Er0120029 Er0200064 Er0201029 Er0210029 Er0300029 "
    "Er1000029 Er1010029 Er1020029 Er1100029 Er1101029 Er1110029 Er1200029 "
    "Er2000029 Er2001029 Er2010029 Er2100029 Es0000029 Es0001029 Es0002029 "
    "Es0003029 Es0010029 Es0011029 Es0012029 Es0020029 Es0021029 Es0030029 "
    "Es0100029 Es0102029 Es0110029 Es0111029 Es0120029 Es0200029 Es0201029 "
    "Es0210029 Es0300029 Es1000047 Es1001047 Es1002047 Es1010047 Es1011047 "
    "Es1020047 Es1100047 Es1101047 Es1110047 Es2000047 Es2001047 Es2010047 "
    "Es2100047 Es3000047 Et0000013 Et0003013 Et0010061 Et0011013 Et0012013 "
    "Et0030013 Et0100050 Et0110050 Et0120050 Et0201050 Et0210050 Et0300050 "
    "Et1000031 Et1010031 Et1020031 Et1100024 Et1101024 Et1110024 Et1200024 "
    "Et2000044 Et2001044 Et2010044 Et2100044 Eu0000044 Eu0001044 Eu0002044 "
    "Eu0003044 Eu0010044 Eu0011044 Eu0012044 Eu0020044 Eu0021044 Eu0030044 "
    "Eu0100080 Eu0102080 Eu0110080 Eu0111080 Eu0120080 Eu0200080 Eu0201080 "
    "Eu0210080 Eu0300080 Eu1000080 Eu1001080 Eu1002080 Eu1010080 Eu1011080 "
    "Eu1020080 Eu1100080 Eu1101080 Eu1110080 Eu1200005 Eu2000080 Eu2001080 "
    "Eu2010080 Eu2100080 Eu3000080 Ev0000069 Ev0001060 Ev0002065 Ev0003069 "
    "Ev0010045 Ev0011069 Ev0012069 Ev0030069 Ev0100069 Ev0101078 Ev0110069 "
    "Ev0120069 Ev0200030 Ev0201069 Ev0210069 Ev0300069 Ev1000008 Ev1001069 "
    "Ev1010008 Ev1020008 Ev1100008 Ev1101008 Ev1110008 Ev1200008 Ev2000008 "
    "Ev2001008 Ev2010008 Ev2100008 Ev3000024 Ew0000031 Ew0001031 Ew0002031 "
    "Ew0003031 Ew0010031 Ew0011031 Ew0012031 Ew0020031 Ew0021031 Ew0030031 "
    "Ew0100031 Ew0101029 Ew0102031 Ew0110031 Ew0111031 Ew0120031 Ew0200031 "
    "Ew0201031 Ew0210031 Ew0300031 Ew1000050 Ew1001050 Ew1002050 Ew1010050 "
    "Ew1011050 Ew1020050 Ew1100026 Ew1101026 Ew1110026 Ew2000032 Ew2001032 "
    "Ew2010032 Ew2100032 Ew3000032 Ex0000009 Ex0001063 Ex0002073 Ex0003009 "
    "Ex0010014 Ex0011009 Ex0012009 Ex0020006 Ex0030009 Ex0100017 Ex0101058 "
    "Ex0102061 Ex0110017 Ex0120017 Ex0200015 Ex0201017 Ex0210017 Ex0300017 "
    "Ex1000027 Ex1001019 Ex1010027 Ex1020027 Ex1100030 Ex1101030 Ex1110030 "
    "Ex1200030 Ex2000011 Ex2001011 Ex2010011 Ex2100011 Ex3000071 "
)

CERT_L17_R0 = (
    "Sa0000172 Sa0001065 Sa0002138 Sa0003021 Sa0004220 Sa0010002 Sa0011028 "
    "Sa0012013 Sa0013204 Sa0020112 Sa0021195 Sa0030092 Sa0100209 Sa0101073 "
    "Sa0102105 Sa0103070 Sa0110112 Sa0111230 Sa0112209 Sa0120205 Sa0200124 "
    "Sa0201137 Sa0202069 Sa0210136 Sa0211142 Sa0300108 Sa1000132 Sa1001069 "
    "Sa1002064 Sa1003014 Sa1010089 Sa1011146 Sa1012021 Sa1100071 Sa1101068 "
    "Sa1200105 Sa2000100 Sb0000172 Sb0001227 Sb0002156 Sb0003146 Sb0004137 "
    "Sb0010011 Sb0011115 Sb0012182 Sb0013137 Sb0020157 Sb0021120 Sb0022156 "
    "Sb0030053 Sb0100029 Sb0101058 Sb0102180 Sb0103196 Sb0110205 Sb0111080 "
    "Sb0120185 Sb0200205 Sb0201227 Sb0202030 Sb0210131 Sb0211084 Sb0300207 "
    "Sb1000024 Sb1001024 Sb1002206 Sb1010108 Sb1011056 Sb1020048 Sb1100115 "
    "Sb1101166 Sb1200193 Sb2000046 Sc0000055 Sc0001182 Sc0002003 Sc0003076 "
    "Sc0004120 Sc0010038 Sc0011061 Sc0012182 Sc0013017 Sc0020148 Sc0021183 "
    "Sc0022028 Sc0030094 Sc0100088 Sc0101188 Sc0102235 Sc0103029 Sc0110125 "
    "Sc0111009 Sc0112216 Sc0120157 Sc0200218 Sc0201026 Sc0202025 Sc0210186 "
    "Sc0211050 Sc0300223 Sc1000153 Sc1001066 Sc1002185 Sc1020054 Sc1100042 "
    "Sc1101017 Sc1200168 Sc2000178 Sd0000016 Sd0001037 Sd0002122 Sd0003041 "
    "Sd0010238 Sd0011009 Sd0012173 Sd0020136 Sd0021120 Sd0030223 Sd0100175 "
    "Sd0101211 Sd0102241 Sd0110208 Sd0111242 Sd0120233 Sd0200211 Sd0201052 "
    "Sd0210205 Sd0300065 Sd1000133 Sd1001105 Sd1010060 Sd1020207 Sd1100012 "
    "Sd1101237 Sd1200185 Sd2000178 Se0000057 Se0001078 Se0002228 Se0003221 "
    "Se0004148 Se0010003 Se0011090 Se0012215 Se0013186 Se0020116 Se0021006 "
    "Se0022022 Se0030025 Se0100075 Se0101188 Se0102085 Se0103027 Se0110134 "
    "Se0111160 Se0112150 Se0120073 Se0200237 Se0201204 Se0202037 Se0210125 "
    "Se0211103 Se0300124 Se1000196 Se1001016 Se1002048 Se1003234 Se1010149 "
    "Se1020106 Se1100055 Se1101125 Se1200140 Se2000101 Sf0000110 Sf0001154 "
    "Sf0002223 Sf0003098 Sf0011062 Sf0012116 Sf0013024 Sf0020050 Sf0021005 "
    "Sf0030075 Sf0100175 Sf0101117 Sf0102072 Sf0110082 Sf0200185 Sf0201140 "
    "Sf0210024 Sf0300022 Sf1000115 Sf1001177 Sf1010103 Sf1020206 Sf1100212 "
    "Sf2000221 Sg0020213 Si0000220 Si0001225 Si0002079 Si0003112 Si0004096 "
    "Si0010048 Si0011145 Si0012192 Si0013163 Si0020197 Si0021223 Si0022228 "
    "Si0030113 Si0100201 Si0101158 Si0102191 Si0103047 Si0110137 Si0111109 "
    "Si0112150 Si0120136 Si0200144 Si0201034 Si0202161 Si0210228 Si0211075 "
    "Si0300017 Si1000242 Si1001055 Si1002107 Si1003189 Si1010070 Si1011074 "
    "Si1020029 Si1100017 Si1101096 Si1102165 Si1200123 Si2000020 Sj0000172 "
    "Sj0001222 Sj0002059 Sj0003010 Sj0004038 Sj0010224 Sj0011186 Sj0012114 "
    "Sj0013174 Sj0020098 Sj0021071 Sj0022022 Sj0030130 Sj0100140 Sj0101150 "
    "Sj0102115 Sj0103112 Sj0110109 Sj0111231 Sj0112127 Sj0120096 Sj0200003 "
    "Sj0201147 Sj0202174 Sj0210213 Sj0211231 Sj0300216 Sj1000167 Sj1001084 "
    "Sj1002080 Sj1010151 Sj1011182 Sj1020044 Sj1100164 Sj1101209 Sj1200054 "
    "Sj2000180 Sk0000036 Sk0001098 Sk0002032 Sk0003079 Sk0010144 Sk0011171 "
    "Sk0012123 Sk0013036 Sk0020004 Sk0021231 Sk0100147 Sk0101133 Sk0102169 "
    "Sk0103077 Sk0110205 Sk0111233 Sk0120119 Sk0200035 Sk0201100 Sk0202023 "
    "Sk0210094 Sk0300236 Sk1000125 Sk1001037 Sk1002136 Sk1010229 Sk1011089 "
    "Sk1020132 Sk1100012 Sk1101193 Sk1200058 Sk2000136 Sk2100205 Sl0000082 "
    "Sl0001018 Sl0002233 Sl0010237 Sl0011234 Sl0020070 Sl0021047 Sl0030238 "
    "Sl0100031 Sl0101080 Sl0102004 Sl0103242 Sl0110118 Sl0111181 Sl0120214 "
    "Sl0200103 Sl0201066 Sl0202119 Sl0210192 Sl0211234 Sl0300122 Sl1000111 "
    "Sl1001225 Sl1002053 Sl1010086 Sl1011043 Sl1020242 Sl1100116 Sl1101018 "
    "Sl1200060 Sl2000139 So0000090 So0100139 Sp0000091 Sp0001118 Sp0002099 "
    "Sp0003101 Sp0004001 Sp0010092 Sp0011088 Sp0012043 Sp0013142 Sp0020104 "
    "Sp0021048 Sp0022117 Sp0030007 Sp0100131 Sp0101060 Sp0102174 Sp0103050 "
    "Sp0110152 Sp0111037 Sp0120051 Sp0200112 Sp0201226 Sp0202093 Sp0210054 "
    "Sp0211122 Sp0300146 Sp1000165 Sp1001032 Sp1010008 Sp1020104 Sp1100182 "
    "Sp1101083 Sp1110219 Sp1200156 Sp2000179 Sp2100119 Sr0000052 Sr0001002 "
    "Sr0002042 Sr0003197 Sr0100216 Sr0101190 Sr0102013 Sr0200201 Sr0201187 "
    "Sr1100078 St0000005 Su0100201 Ua0000071 Ua0001205 Ua0002201 Ua0003159 "
    "Ua0010205 Ua0011047 Ua0012043 Ua0020239 Ua0030048 Ua0100097 Ua0101191 "
    "Ua0102135 Ua0110137 Ua0120037 Ua0200098 Ua0201139 Ua0210114 Ua0300060 "
    "Ua1001075 Ua1020183 Ua1101172 Ua1200183 Ub0000241 Ub0001097 Ub0002183 "
    "Ub0010102 Ub0011098 Ub0020227 Ub0021140 Ub0030016 Ub0100115 Ub0101038 "
    "Ub0102174 Ub0110168 Ub0200155 Ub0201100 Ub0300210 Ub1000156 Ub1001078 "
    "Ub1010121 Ub1011162 Ub1100205 Ub1200144 Ub2000104 Uc0000204 Uc0001177 "
    "Uc0002072 Uc0003147 Uc0004191 Uc0010232 Uc0011002 Uc0012232 Uc0013213 "
    "Uc0020068 Uc0021174 Uc0030191 Uc0100166 Uc0101182 Uc0102216 Uc0103059 "
    "Uc0110191 Uc0111128 Uc0120185 Uc0200032 Uc0201165 Uc0202050 Uc0210221 "
    "Uc0211133 Uc0300241 Uc1000147 Uc1001234 Uc1002131 Uc1010039 Uc1011126 "
    "Uc1020201 Uc1100048 Uc1101156 Uc1200156 Uc2000035 Ud0000224 Ud0001152 "
    "Ud0011074 Ud0030073 Ud0200168 Ud1000174 Ue0000209 Ue0001128 Ue0002068 "
    "Ue0011209 Ue0100086 Ue0101172 Ue0200177 Ue0201137 Uf0000170 Uf0001115 "
    "Ug1010175 Ug1020208 Ug1200095 Ug2000091 Ug2002126 Ug4000007 Uh0102147 "
    "Ui0004144 Ui0012118 Ui0100026 Ui0110173 Ui0120101 Ui0200234 Ui0201046 "
    "Ui0300134 Ui1002118 Ui1010186 Ui1100016 Ui1101187 Ui1111215 Uj0030134 "
    "Uj4000071 Uk0000091 Uk0021207 Uk0022140 Uk0100053 Uk0110010 Uk0111169 "
    "Uk0112160 Uk0200238 Uk0201096 Uk0211242 Uk1011202 Uk2011002 Ul0012214 "
    "Ul3010194 Um0010147 Um0011058 Um0020239 Um0021043 Um0100157 Um0101002 "
    "Um0102069 Um0111076 Um0112068 Um0130003 Um0200035 Um0202062 Um0211203 "
    "Um1000200 Um1001062 Um1010093 Um1020009 Um2000155 Un0002139 Uo0000073 "
    "Uo0004233 Uo0010112 Uo0012086 Uo0020093 Uo0021031 Uo0022076 Uo0100171 "
    "Uo0110200 Uo0120180 Uo1111075 Uo3010001 Uo4000084 Up1020037 Up2000149 "
    "Up2002016 Up3000067 Up3001101 Up4000020 Uq0000212 Uq0002222 Uq0004183 "
    "Uq0010031 Uq0011079 Uq0012022 Uq0021183 Uq0022133 Uq0100077 Uq0102084 "
    "Uq0110046 Uq0200172 Uq0201177 Uq0211223 Uq1100051 Uq1102235 Uq1111150 "
    "Uq2101146 Ur0020003 Ur0100021 Ur2100189 Ur3010169 Us0001022 Us0010064 "
    "Us0011125 Us0020198 Us0030110 Us1010197 Ut1100133 Ut1102081 Ut2000125 "
    "Ut2001143 Ut2011050 Ut2101223 Ut3000196 Ut3001107 Uu0000117 Uu0001093 "
    "Uu0004148 Uu0010125 Uu0012015 Uu0020114 Uu0100123 Uu0101031 Uu0110144 "
    "Uu0120097 Uu1000167 Uu1010216 Uu4000013 Uw0000071 Uw0002019 Uw0004061 "
    "Uw0021040 Uw0100076 Uw0102174 Uw0211027 Uw1102228 Uw1111119 Ux0100021 "
    "Ux0120049 Ux1000081 Ux1002173 Ux1100088 Ux1101031 Ux1111235 Ux2000033 "
    "Ux2001091 Ux2100080 Ux3000104 Ux3010111 Ux4000137 Ea0020081 Eb0102006 "
    "Eb1011235 Eb1100142 Eb1200119 Eb2000168 Eb2001025 Ec0000111 Ec0001057 "
    "Ec0010135 Ec0012162 Ec0110046 Ec1002238 Ec1010177 Ed0030140 Ed0200147 "
    "Ed1000093 Ed1001171 Ed1010127 Ed1020237 Ed1100132 Ed1101060 Ed1200072 "
    "Ed3000089 Ee0000111 Ee0002048 Ee0100015 Ee0102015 Ee0110064 Ef1000162 "
    "Ef1010215 Eh0100081 Ei0010090 Ei1010192 Ei3010086 Ej0020059 Ej0021047 "
    "Ej0030173 Ej0111183 Ej0112220 Ej0200088 Ej0202049 Ej0211120 Ej0300223 "
    "Ej1000085 Ej1001057 Ej1010005 Ej1020151 Ej1200180 Ej2000214 Ej4000222 "
    "Ek0002003 Ek0004012 Ek0102231 Ek0110192 Ek2101196 El0010056 El0012163 "
    "El0100195 El0101186 El0110143 El0111132 El0120122 El0200164 El0201075 "
    "El0202084 El0300050 El1000137 El1002080 El1010014 El1100065 El1101104 "
    "El1111168 El3000090 Em0030164 Em0211129 Em4000105 En0000110 En0002216 "
    "En0021201 En0022029 En0100019 En0102233 En0110024 En0111127 En0112068 "
    "En0120009 En0200020 En0201049 En1011090 En1100188 En1102196 En2011216 "
    "Eo0012168 Eo0020092 Eo3000142 Eo3010147 Ep0010226 Ep0011001 Ep0020200 "
    "Ep0021154 Ep0030159 Ep0100002 Ep0101160 Ep0102104 Ep0111045 Ep0112032 "
    "Ep0200074 Ep0202006 Ep0211147 Ep1000114 Ep1001010 Ep1010156 Ep1011196 "
    "Ep1020156 Ep2000016 Ep2002118 Ep2011148 Eq0002228 Eq0004143 Eq0110079 "
    "Eq2101091 Er0000120 Er0001021 Er0010033 Er0012014 Er0100012 Er0101090 "
    "Er0110193 Er0111042 Er0120228 Er0300226 Er1000026 Er1002054 Es1020069 "
    "Et0000112 Et0010135 Et0100066 Et0200166 Et0201122 Et1100008 Eu0020206 "
    "Eu1002111 Eu1111202 Eu2100167 Eu3000152 Eu3010229 Eu4000126 Ev0000046 "
    "Ev0001094 Ev0002138 Ev0010173 Ev0011124 Ev0020011 Ev0021238 Ev0030138 "
    "Ev0111219 Ev0112063 Ev0200085 Ev0202074 Ev1010111 Ev1011226 Ev1020146 "
    "Ev2002162 Ev2011209 Ew0001240 Ew0002240 Ew0003240 Ew0010240 Ew0011240 "
    "Ew0012240 Ew0013240 Ew0020240 Ew0021240 Ew0022240 Ew0030240 Ew0031240 "
    "Ew0040240 Ew0100240 Ew0101240 Ew0102240 Ew0103240 Ew0110240 Ew0111240 "
    "Ew0112240 Ew0120240 Ew0121240 Ew0130240 Ew0200240 Ew0201240 Ew0202240 "
    "Ew0210240 Ew0211240 Ew0220240 Ew0300240 Ew0310240 Ew0400240 Ew1000240 "
    "Ew1001240 Ew1002240 Ew1003240 Ew1010240 Ew1011240 Ew1012240 Ew1020240 "
    "Ew1021240 Ew1100083 Ew1101240 Ew1110240 Ew1111240 Ew1120240 Ew1200240 "
    "Ew1201240 Ew1210240 Ew1300240 Ew2000229 Ew2002240 Ew2010240 Ew2100240 "
    "Ew2110240 Ew3100240 Ew4000240 Ex0000184 Ex0001228 Ex0002240 Ex0003240 "
    "Ex0010135 Ex0011240 Ex0012088 Ex0013240 Ex0020166 Ex0021240 Ex0022240 "
    "Ex0030240 Ex0031240 Ex0040240 Ex0100177 Ex0101070 Ex0102240 Ex0103240 "
    "Ex0110034 Ex0111006 Ex0112240 Ex0121240 Ex0130240 Ex0200240 Ex0201240 "
    "Ex0202240 Ex0210240 Ex0211240 Ex0220240 Ex0300240 Ex0301240 Ex0310240 "
    "Ex1000133 Ex1001240 Ex1002030 Ex1003240 Ex1010005 Ex1011240 Ex1012240 "
    "Ex1020240 Ex1021240 Ex1030240 Ex1100240 Ex1101240 Ex1102240 Ex1110240 "
    "Ex1111240 Ex1120240 Ex1200240 Ex1210240 Ex2000240 Ex2001240 Ex2002240 "
    "Ex2010240 Ex2011240 Ex2020240 Ex2100240 Ex2101240 Ex2110240 Ex2200240 "
    "Ex3000240 Ex3001240 Ex3010240 Ex3100240 Ex4000127 "
)

CERT_L17_R1 = (
    "Sa0000118 Sa0001182 Sa0002087 Sa0003177 Sa0004207 Sa0010218 Sa0011226 "
    "Sa0012054 Sa0013046 Sa0020082 Sa0021237 Sa0022222 Sa0030023 Sa0100068 "
    "Sa0101040 Sa0102119 Sa0103154 Sa0110080 Sa0111031 Sa0120026 Sa0121119 "
    "Sa0200027 Sa0201056 Sa0202084 Sa0210025 Sa0300193 Sa1000054 Sa1001084 "
    "Sa1002038 Sa1003051 Sa1010230 Sa1011059 Sa1012033 Sa1100194 Sa1101214 "
    "Sa1200213 Sa2000052 Sb0000145 Sb0001128 Sb0002150 Sb0003149 Sb0004154 "
    "Sb0010056 Sb0011091 Sb0012197 Sb0013148 Sb0020037 Sb0021111 Sb0022173 "
    "Sb0030098 Sb0100023 Sb0101061 Sb0102106 Sb0103099 Sb0110221 Sb0111068 "
    "Sb0120103 Sb0200209 Sb0201033 Sb0202170 Sb0210023 Sb0300139 Sb1000006 "
    "Sb1001129 Sb1002155 Sb1010190 Sb1011223 Sb1020021 Sb1100199 Sb1101090 "
    "Sb1200028 Sb2000052 Sc0000153 Sc0001231 Sc0002065 Sc0003119 Sc0004109 "
    "Sc0010209 Sc0011001 Sc0012232 Sc0013232 Sc0020226 Sc0021084 Sc0022147 "
    "Sc0030148 Sc0100217 Sc0101047 Sc0102070 Sc0103109 Sc0110171 Sc0111184 "
    "Sc0120017 Sc0200044 Sc0201064 Sc0202065 Sc0210119 Sc0300037 Sc1000099 "
    "Sc1001066 Sc1002085 Sc1020015 Sc1100144 Sc1102045 Sc1110105 Sc1200108 "
    "Sc2000076 Sd0000160 Sd0001175 Sd0002050 Sd0003034 Sd0010094 Sd0011231 "
    "Sd0012096 Sd0020019 Sd0021075 Sd0030064 Sd0100226 Sd0101226 Sd0102232 "
    "Sd0110060 Sd0111210 Sd0120194 Sd0200194 Sd0201077 Sd0210202 Sd0300073 "
    "Sd1000199 Sd1001201 Sd1010018 Sd1020106 Sd1100125 Sd1101108 Sd1200189 "
    "Sd2000010 Se0000188 Se0001016 Se0002107 Se0003057 Se0004161 Se0010084 "
    "Se0011162 Se0012240 Se0013032 Se0020056 Se0021009 Se0022227 Se0030106 "
    "Se0100209 Se0101123 Se0102142 Se0103212 Se0110035 Se0111104 Se0120010 "
    "Se0200078 Se0201026 Se0202211 Se0210186 Se0300030 Se1000111 Se1001128 "
    "Se1002096 Se1003199 Se1010151 Se1011071 Se1020188 Se1100176 Se1101152 "
    "Se1200116 Se2000101 Sf0000044 Sf0001142 Sf0002175 Sf0003050 Sf0010180 "
    "Sf0011131 Sf0012120 Sf0020080 Sf0021005 Sf0022099 Sf0030006 Sf0100121 "
    "Sf0101228 Sf0102242 Sf0103114 Sf0110205 Sf0200221 Sf0201002 Sf0300199 "
    "Sf1000022 Sf1001138 Sf1010037 Sf1020059 Sf1100071 Sf2000092 Sg0020180 "
    "Si0000121 Si0001183 Si0002235 Si0003196 Si0004153 Si0010039 Si0011094 "
    "Si0012221 Si0013018 Si0020122 Si0021169 Si0022069 Si0030161 Si0100072 "
    "Si0101107 Si0102236 Si0103138 Si0110060 Si0111161 Si0120185 Si0200117 "
    "Si0202111 Si0210127 Si0300092 Si1000101 Si1001088 Si1002002 Si1003225 "
    "Si1010166 Si1011108 Si1012091 Si1020119 Si1100056 Si1101099 Si1200162 "
    "Si2000182 Sj0000199 Sj0001051 Sj0002116 Sj0003228 Sj0004182 Sj0010125 "
    "Sj0011150 Sj0012197 Sj0013090 Sj0020158 Sj0021101 Sj0022211 Sj0030046 "
    "Sj0100143 Sj0101039 Sj0102164 Sj0103019 Sj0110019 Sj0111100 Sj0120075 "
    "Sj0200237 Sj0201090 Sj0202036 Sj0210166 Sj0300117 Sj1000140 Sj1001159 "
    "Sj1002230 Sj1010052 Sj1011041 Sj1020179 Sj1100027 Sj1101215 Sj1200033 "
    "Sj2000210 Sk0000045 Sk0001134 Sk0002155 Sk0003112 Sk0010225 Sk0011078 "
    "Sk0012169 Sk0020097 Sk0021027 Sk0100088 Sk0101051 Sk0102103 Sk0103079 "
    "Sk0110062 Sk0111233 Sk0120131 Sk0200179 Sk0201159 Sk0202108 Sk0210208 "
    "Sk0300047 Sk1000095 Sk1001208 Sk1002221 Sk1010052 Sk1011190 Sk1020049 "
    "Sk1100033 Sk1101148 Sk1110240 Sk1200013 Sk2000079 Sk2100065 Sl0000085 "
    "Sl0001060 Sl0002131 Sl0003240 Sl0010213 Sl0011021 Sl0020097 Sl0021179 "
    "Sl0022195 Sl0030088 Sl0100095 Sl0101207 Sl0102114 Sl0103155 Sl0110151 "
    "Sl0111035 Sl0120154 Sl0200230 Sl0201230 Sl0210002 Sl0300128 Sl1000048 "
    "Sl1001123 Sl1010149 Sl1011023 Sl1020104 Sl1100074 Sl1101184 Sl1200081 "
    "Sl2000118 So0000195 So0100021 Sp0000142 Sp0001143 Sp0002158 Sp0003159 "
    "Sp0004005 Sp0010137 Sp0011027 Sp0012222 Sp0013152 Sp0020128 Sp0021094 "
    "Sp0030031 Sp0100137 Sp0101135 Sp0102148 Sp0103099 Sp0110158 Sp0111127 "
    "Sp0120080 Sp0200019 Sp0201059 Sp0202211 Sp0210130 Sp0300230 Sp1000114 "
    "Sp1001240 Sp1002128 Sp1010235 Sp1020206 Sp1100098 Sp1101168 Sp1200204 "
    "Sp2000014 Sp2100129 Sr0000169 Sr0001057 Sr0002159 Sr0003108 Sr0100087 "
    "Sr0101201 Sr0200144 Sr0201117 Sr1100063 St0000104 Su0100071 Ua0000071 "
    "Ua0001178 Ua0002105 Ua0010106 Ua0011062 Ua0012101 Ua0020080 Ua0030238 "
    "Ua0100004 Ua0101089 Ua0110055 Ua0200047 Ua0201091 Ua0210236 Ua0300233 "
    "Ua1001078 Ua1020076 Ua1101115 Ua1200126 Ub0000233 Ub0001077 Ub0002033 "
    "Ub0010131 Ub0011170 Ub0020167 Ub0030001 Ub0100094 Ub0101008 Ub0102071 "
    "Ub0110090 Ub0200232 Ub0201207 Ub0210192 Ub0300134 Ub1000198 Ub1001099 "
    "Ub1010052 Ub1011120 Ub1100109 Ub1101226 Ub1200192 Ub2000140 Uc0000102 "
    "Uc0001189 Uc0002213 Uc0003042 Uc0004010 Uc0010025 Uc0011161 Uc0012097 "
    "Uc0013059 Uc0020080 Uc0021081 Uc0030020 Uc0100124 Uc0101182 Uc0102123 "
    "Uc0103164 Uc0110176 Uc0111176 Uc0120185 Uc0200083 Uc0201019 Uc0202019 "
    "Uc0210110 Uc0300079 Uc1000219 Uc1001120 Uc1002024 Uc1010074 Uc1011059 "
    "Uc1020102 Uc1100051 Uc1200096 Uc2000017 Ud0000188 Ud0001050 Ud0011205 "
    "Ud0030091 Ud0100108 Ud0200072 Ud1000227 Ue0000150 Ue0001088 Ue0011026 "
    "Ue0100142 Ue0101061 Ue0200105 Ue2011057 Uf0000182 Uf0001130 Ug0202131 "
    "Ug1010034 Ug1120013 Ug1200032 Ug2000231 Ug2002017 Ug4000192 Uh0102074 "
    "Uh0110040 Ui0110174 Ui0120224 Ui0200019 Ui0201123 Ui0300117 Ui1000026 "
    "Ui1002120 Ui1010151 Ui1100223 Ui1101071 Ui2200205 Ui3000190 Uj0030034 "
    "Uj4000154 Uk0000151 Uk0002027 Uk0021078 Uk0022113 Uk0110126 Uk0111190 "
    "Uk0200121 Uk0201086 Uk1011235 Uk2011201 Ul0012215 Ul2200178 Ul3010012 "
    "Um0010030 Um0011224 Um0020155 Um0021031 Um0100105 Um0101014 Um0102120 "
    "Um0111114 Um0200143 Um0202101 Um1000175 Um1001161 Um1010077 Um1011224 "
    "Um1020018 Um2000205 Un0002139 Un0110135 Un2101184 Uo0001155 Uo0004208 "
    "Uo0010218 Uo0012093 Uo0020156 Uo0021165 Uo0022118 Uo0100081 Uo0110114 "
    "Uo0111127 Uo0120131 Uo3010117 Uo4000232 Up1020142 Up2000137 Up2002170 "
    "Up3000181 Up3001239 Up4000052 Uq0000116 Uq0002234 Uq0004093 Uq0010055 "
    "Uq0011178 Uq0012132 Uq0021186 Uq0022120 Uq0040039 Uq0100031 Uq0102026 "
    "Uq0110228 Uq0200037 Uq0201032 Uq1100126 Uq1102213 Uq2101083 Uq2200042 "
    "Ur0020096 Ur0100024 Ur2200229 Ur3000067 Ur3010103 Us0001145 Us0010010 "
    "Us0011086 Us0020006 Us0030089 Us0111054 Us1010084 Ut1100162 Ut1102190 "
    "Ut2000131 Ut2001203 Ut2011237 Ut2101044 Ut3000114 Ut3001094 Uu0000194 "
    "Uu0001015 Uu0004074 Uu0010233 Uu0012137 Uu0020165 Uu0100220 Uu0101146 "
    "Uu0110136 Uu0111114 Uu0120199 Uu1000009 Uu1010060 Uu1201006 Uv0202118 "
    "Uv2100221 Uw0000044 Uw0002184 Uw0004239 Uw0021052 Uw0022019 Uw0100088 "
    "Uw0102001 Uw1102242 Uw2200133 Ux0100078 Ux0120232 Ux1000105 Ux1002183 "
    "Ux1100123 Ux1120070 Ux1201031 Ux2000165 Ux2001094 Ux2100128 Ux2200089 "
    "Ux3000215 Ux3010086 Ux4000025 Eb0102073 Eb1100175 Eb1200071 Eb2000018 "
    "Ec0000007 Ec0001086 Ec0010009 Ec0012112 Ec0110049 Ec1010037 Ed0030110 "
    "Ed0200043 Ed1000009 Ed1001057 Ed1010190 Ed1020023 Ed1100214 Ed1101239 "
    "Ed1200172 Ee0000093 Ee0002097 Ee0100216 Ee0102225 Ee0110168 Ef1000219 "
    "Ef1010073 Eg0020090 Eh0100198 Eh0200143 Ei0010186 Ei1010096 Ei3010066 "
    "Ej0020113 Ej0021008 Ej0030176 Ej0111095 Ej0200085 Ej0202092 Ej0300125 "
    "Ej1000094 Ej1001219 Ej1010134 Ej1011024 Ej1020075 Ej1200027 Ej2000199 "
    "Ej2002094 Ej4000116 Ek0000216 Ek0002042 Ek0004111 Ek0102041 Ek0110046 "
    "Ek2101191 El0004026 El0010131 El0012102 El0100177 El0101006 El0110051 "
    "El0111045 El0120031 El0200238 El0201145 El0300238 El1000242 El1002181 "
    "El1010098 El1100230 El1101080 El1120094 El2200113 El3000234 El4000055 "
    "Em0030074 Em2002101 Em4000025 En0000212 En0002057 En0021216 En0022229 "
    "En0100073 En0102150 En0110209 En0111176 En0120025 En0200070 En0201169 "
    "En1011116 En1100107 En1102213 En2011021 En2200228 Eo0012173 Eo0020089 "
    "Eo2200147 Eo3000223 Eo3010008 Ep0010006 Ep0011233 Ep0020198 Ep0021213 "
    "Ep0030135 Ep0100128 Ep0101198 Ep0102090 Ep0111119 Ep0200167 Ep0202121 "
    "Ep1000213 Ep1001184 Ep1010170 Ep1011228 Ep1020085 Ep2000109 Ep2002157 "
    "Ep2011011 Eq0002192 Eq0004051 Eq0110006 Eq2101107 Er0000030 Er0001128 "
    "Er0004222 Er0010094 Er0012210 Er0100117 Er0101053 Er0110198 Er0120143 "
    "Er0300169 Er1000188 Er1002089 Es1020137 Et0000239 Et0010198 Et0100055 "
    "Et0200229 Eu0020242 Eu1002229 Eu1120063 Eu1201161 Eu2100159 Eu2200176 "
    "Eu3000099 Eu3010128 Eu4000147 Ev0000202 Ev0001061 Ev0002065 Ev0010069 "
    "Ev0011163 Ev0020055 Ev0021062 Ev0030206 Ev0111238 Ev0200166 Ev0202116 "
    "Ev1010147 Ev1011029 Ev1020140 Ev2002151 Ev2011233 Ew0001204 Ew0002204 "
    "Ew0003204 Ew0004109 Ew0010204 Ew0011204 Ew0012204 Ew0013204 Ew0020204 "
    "Ew0021204 Ew0022204 Ew0030204 Ew0031204 Ew0040204 Ew0100204 Ew0101204 "
    "Ew0102204 Ew0103204 Ew0110204 Ew0111204 Ew0112204 Ew0120204 Ew0121204 "
    "Ew0130204 Ew0200204 Ew0201204 Ew0202204 Ew0210204 Ew0211204 Ew0220204 "
    "Ew0300204 Ew0310204 Ew0400204 Ew1000204 Ew1001204 Ew1002204 Ew1003204 "
    "Ew1010204 Ew1011204 Ew1012204 Ew1020204 Ew1021204 Ew1100037 Ew1101204 "
    "Ew1110204 Ew1111204 Ew1120204 Ew1200204 Ew1201204 Ew1210204 Ew1300204 "
    "Ew2000070 Ew2002204 Ew2010204 Ew2100204 Ew2110204 Ew3000074 Ew3100204 "
    "Ew4000204 Ex0000202 Ex0001023 Ex0002204 Ex0003204 Ex0004015 Ex0010161 "
    "Ex0011204 Ex0012213 Ex0013204 Ex0020147 Ex0021204 Ex0022204 Ex0030204 "
    "Ex0031204 Ex0040204 Ex0100006 Ex0101194 Ex0102204 Ex0103204 Ex0110089 "
    "Ex0111107 Ex0112204 Ex0120039 Ex0121204 Ex0130204 Ex0200204 Ex0201204 "
    "Ex0202204 Ex0210204 Ex0211204 Ex0220204 Ex0300204 Ex0301204 Ex0310204 "
    "Ex1000079 Ex1001204 Ex1002011 Ex1003204 Ex1010088 Ex1011204 Ex1012204 "
    "Ex1020204 Ex1021204 Ex1030204 Ex1100204 Ex1101204 Ex1102204 Ex1110204 "
    "Ex1111204 Ex1120204 Ex1200204 Ex1201091 Ex1210204 Ex2000204 Ex2001204 "
    "Ex2002204 Ex2010204 Ex2011204 Ex2020204 Ex2100204 Ex2101204 Ex2110204 "
    "Ex2200204 Ex3000204 Ex3001204 Ex3010204 Ex3100204 Ex4000084 "
)

CERT_L7_R2M = (
    "Sa0000050 Sa0001066 Sa0002028 Sa0003055 Sa0010030 Sa0011020 Sa0012077 "
    "Sa0020023 Sa0100014 Sa0101062 Sa0102013 Sa0110022 Sa0111050 Sa0200036 "
    "Sa1000009 Sa1001047 Sa1010006 Sa1100018 Sb0000024 Sb0001065 Sb0002026 "
    "Sb0003016 Sb0010040 Sb0011029 Sb0012011 Sb0020077 Sb0100069 Sb0101043 "
    "Sb0102034 Sb0110006 Sb0200005 Sb0201016 Sb1000063 Sb1001023 Sb1010065 "
    "Sb1100052 Sc0001080 Sc0002037 Sc0003038 Sc0010078 Sc0011039 Sc0012028 "
    "Sc0020020 Sc0100011 Sc0101035 Sc0102033 Sc0110075 Sc0120034 Sc0200019 "
    "Sc0210038 Sc1000027 Sc1001012 Sc1010032 Sc1100058 Sd0000078 Sd0001016 "
    "Sd0002058 Sd0003014 Sd0010075 Sd0011072 Sd0012007 Sd0020017 Sd0100010 "
    "Sd0101068 Sd0110075 Sd0200007 Sd1000045 Sd1001067 Sd1010044 Sd1100077 "
    "Se0000071 Se0001055 Se0002003 Se0003060 Se0010002 Se0011005 Se0012004 "
    "Se0020079 Se0100066 Se0101033 Se0102047 Se0120064 Se0200009 Se0201039 "
    "Se1000027 Se1001045 Se1010036 Se1100018 Se2000013 Sf0000079 Sf0001072 "
    "Sf0010056 Sf0011013 Sf0020064 Sf0100072 Sf0101012 Sf0110005 Sf0200063 "
    "Sf0210050 Sf1000071 Sf1010037 Sf1100005 Sg0100047 Sh0100023 Si0000075 "
    "Si0001023 Si0002063 Si0003002 Si0010063 Si0011060 Si0012021 Si0020051 "
    "Si0100003 Si0101069 Si0102034 Si0110068 Si0111006 Si0200018 Si1000017 "
    "Si1001071 Si1010071 Si1100003 Sj0000015 Sj0001062 Sj0002016 Sj0011024 "
    "Sj0012039 Sj0020008 Sj0100061 Sj0101039 Sj0102066 Sj0110030 Sj0200057 "
    "Sj1000045 Sj1001006 Sj1010020 Sj1100073 Sk0000080 Sk0001070 Sk0002012 "
    "Sk0010062 Sk0011016 Sk0020074 Sk0100003 Sk0101023 Sk0110057 Sk0200030 "
    "Sk1000058 Sk1001017 Sk1010062 Sk1100040 Sl0000033 Sl0001056 Sl0002008 "
    "Sl0010051 Sl0011019 Sl0020011 Sl0100059 Sl0101061 Sl0110076 Sl0200009 "
    "Sl1000021 Sl1010012 Sl1100006 Sm0000002 Sn0100065 Sp0000060 Sp0001009 "
    "Sp0002003 Sp0003045 Sp0010017 Sp0011009 Sp0020006 Sp0100035 Sp0101048 "
    "Sp0110078 Sp0200057 Sp0210047 Sp1000046 Sp1010055 Sp1100070 Sq0100041 "
    "Sr0000066 Sr0001047 Sr0010032 Sr0011001 Sr0020037 Sr0100030 Sr0101071 "
    "Sr0110017 Sr0200072 Sr0210031 Su0100005 Sw0100033 Sx0000071 Ua0000034 "
    "Ua0010019 Ua0011005 Ua0020043 Ua0100012 Ua0110075 Ua0200030 Ua1000069 "
    "Ua1010055 Ua1100032 Ub0000057 Ub0001055 Ub0002002 Ub0010036 Ub0011046 "
    "Ub0020001 Ub0100007 Ub0101001 Ub0110039 Ub0200060 Ub1000030 Ub1010018 "
    "Ub1100015 Uc0000031 Uc0001048 Uc0002058 Uc0010001 Uc0011014 Uc0012033 "
    "Uc0020052 Uc0100038 Uc0101012 Uc0102033 Uc0110078 Uc0200080 Uc0201036 "
    "Uc1000075 Uc1010046 Uc1100056 Ud0000041 Ud0001043 Ud0010029 Ud0011079 "
    "Ud0020080 Ud0100007 Ud0101012 Ud0102035 Ud0200006 Ud1000043 Ud1010063 "
    "Ud1100030 Ue0000061 Ue0001050 Ue0010067 Ue0011055 Ue0020008 Ue0100033 "
    "Ue0101033 Ue0200033 Ue1010078 Ue1100051 Uf0000034 Uf0001079 Uf0010040 "
    "Uf0011051 Uf0020015 Uf0100069 Uf0101043 Uf0102075 Uf0200003 Ug0201069 "
    "Ug1020057 Ug2000009 Uh0000078 Uh0002008 Uh0100069 Ui1101023 Ui2000046 "
    "Uj0002076 Uj0100009 Uj0102066 Uj1002047 Uk1101041 Uk2000003 Ul0000011 "
    "Ul0002022 Ul0030003 Ul0100035 Ul0102035 Ul1002029 Um1101006 Um2000004 "
    "Um3000048 Un0000056 Un0002030 Un0010050 Uo1101039 Uo2000078 Uo2001063 "
    "Uo3000049 Up0000046 Up0002015 Up0010064 Up0100010 Up0102075 Up1002010 "
    "Up3000046 Uq1101076 Uq2000041 Uq3000046 Ur0000016 Ur0002053 Ur0010025 "
    "Ur0100053 Us2000034 Ut0000042 Ut0002023 Ut0010031 Ut0102039 Uu1101072 "
    "Uu2000037 Uu3000007 Uw1101021 Uw2000075 Uw3000066 Ux0000059 Ux0002038 "
    "Ux0010019 Ux0100007 Ux0102067 Ux0200034 Ux0201034 Ux0210034 Ux0300034 "
    "Ux1000035 Ux1001035 Ux1010069 Ux1011069 Ux1020069 Ux1100069 Ux1101069 "
    "Ux1110069 Ux1200069 Ux2000069 Ux2001069 Ux2010069 Ux2100069 Ea0000069 "
    "Ea0001069 Ea0002069 Ea0003069 Ea0010069 Ea0011069 Ea0012069 Ea0020069 "
    "Ea0021069 Ea0030069 Ea0100069 Ea0101069 Ea0102069 Ea0110069 Ea0111069 "
    "Ea0120069 Ea0200069 Ea0210069 Ea0300069 Ea1000069 Ea1001069 Ea1002069 "
    "Ea1010069 Ea1100069 Ea1110069 Ea1200069 Ea2010069 Ea2100069 Eb0000048 "
    "Eb0001069 Eb0003069 Eb0010018 Eb0011069 Eb0012069 Eb0020069 Eb0021069 "
    "Eb0100080 Eb0101069 Eb0110069 Eb0111069 Eb0120069 Eb0200069 Eb0201069 "
    "Eb0210069 Eb0300069 Eb1000069 Eb1001069 Eb1010069 Eb1011069 Eb1020069 "
    "Eb1100069 Eb1101069 Eb1110069 Eb1200069 Eb2000069 Eb2001069 Eb2010069 "
    "Eb2100069 Ec0000069 Ec0001069 Ec0002069 Ec0003069 Ec0010069 Ec0011069 "
    "Ec0012069 Ec0020069 Ec0021069 Ec0030069 Ec0100069 Ec0101069 Ec0102069 "
    "Ec0110069 Ec0111069 Ec0120069 Ec0200069 Ec0201047 Ec0210069 Ec0300069 "
    "Ec1000069 Ec1001069 Ec1002069 Ec1010069 Ec1100069 Ec1110069 Ec1200069 "
    "Ec2000043 Ec2010069 Ec2100069 Ed0000048 Ed0001069 Ed0002065 Ed0003069 "
    "Ed0010061 Ed0011069 Ed0012069 Ed0020069 Ed0021069 Ed0100047 Ed0101069 "
    "Ed0102063 Ed0110069 Ed0111069 Ed0120069 Ed0200069 Ed0201069 Ed0210069 "
    "Ed0300069 Ed1000069 Ed1001069 Ed1010069 Ed1011069 Ed1020069 Ed1100069 "
    "Ed1101069 Ed1110069 Ed1200069 Ed2000069 Ed2001069 Ed2010069 Ed2100069 "
    "Ee0000069 Ee0001069 Ee0002069 Ee0003069 Ee0010069 Ee0011069 Ee0012069 "
    "Ee0020069 Ee0021069 Ee0030069 Ee0100069 Ee0101069 Ee0102069 Ee0110069 "
    "Ee0111069 Ee0120069 Ee0200069 Ee0210069 Ee0300069 Ee1000069 Ee1001069 "
    "Ee1002069 Ee1010069 Ee1100069 Ee1110069 Ee1200069 Ee2010069 Ee2100069 "
    "Ef0000036 Ef0001069 Ef0003069 Ef0010059 Ef0011069 Ef0012069 Ef0020069 "
    "Ef0021069 Ef0100073 Ef0101069 Ef0110069 Ef0111069 Ef0120069 Ef0200069 "
    "Ef0201069 Ef0210069 Ef0300069 Ef1000069 Ef1001069 Ef1010069 Ef1011069 "
    "Ef1020069 Ef1100069 Ef1101069 Ef1110069 Ef1200069 Ef2000069 Ef2001069 "
    "Ef2010069 Ef2100069 Eg0000069 Eg0001069 Eg0002069 Eg0003069 Eg0010069 "
    "Eg0011069 Eg0012069 Eg0020069 Eg0021069 Eg0030069 Eg0100069 Eg0101069 "
    "Eg0102069 Eg0110069 Eg0111069 Eg0120069 Eg0200069 Eg0210069 Eg0300069 "
    "Eg1000069 Eg1001069 Eg1002069 Eg1010069 Eg1100069 Eg1110069 Eg1200069 "
    "Eg2010069 Eg2100069 Eh0000061 Eh0001069 Eh0003069 Eh0010072 Eh0011069 "
    "Eh0012069 Eh0020069 Eh0021069 Eh0100061 Eh0101069 Eh0110069 Eh0111069 "
    "Eh0120069 Eh0200069 Eh0201069 Eh0210069 Eh0300069 Eh1000069 Eh1001069 "
    "Eh1010069 Eh1011069 Eh1020069 Eh1100069 Eh1101069 Eh1110069 Eh1200069 "
    "Eh2000069 Eh2001069 Eh2010069 Eh2100069 Ei0000069 Ei0001069 Ei0002069 "
    "Ei0003069 Ei0010069 Ei0011069 Ei0012069 Ei0020069 Ei0021069 Ei0030069 "
    "Ei0100069 Ei0101069 Ei0102069 Ei0110069 Ei0111069 Ei0120069 Ei0200069 "
    "Ei0201054 Ei0210069 Ei0300069 Ei1000069 Ei1001069 Ei1002069 Ei1010069 "
    "Ei1100069 Ei1110069 Ei1200069 Ei2000018 Ei2001075 Ei2010069 Ei2100069 "
    "Ej0000029 Ej0001069 Ej0002038 Ej0003069 Ej0010025 Ej0011069 Ej0012069 "
    "Ej0020069 Ej0021069 Ej0100068 Ej0101069 Ej0102025 Ej0110069 Ej0111069 "
    "Ej0120069 Ej0200069 Ej0201069 Ej0210069 Ej0300069 Ej1000069 Ej1001069 "
    "Ej1002057 Ej1010069 Ej1011069 Ej1020069 Ej1100069 Ej1101069 Ej1110069 "
    "Ej1200069 Ej2000069 Ej2001069 Ej2010069 Ej2100069 Ek0000069 Ek0001069 "
    "Ek0002069 Ek0003069 Ek0010069 Ek0011069 Ek0012069 Ek0020069 Ek0021069 "
    "Ek0030069 Ek0100069 Ek0101069 Ek0102069 Ek0110069 Ek0111069 Ek0120069 "
    "Ek0200069 Ek0210069 Ek0300069 Ek1000069 Ek1001069 Ek1002069 Ek1010069 "
    "Ek1100069 Ek1110069 Ek1200069 Ek2000075 Ek2010069 Ek2100069 Ek3000018 "
    "El0000042 El0001069 El0002070 El0003069 El0010007 El0011069 El0012069 "
    "El0020069 El0021069 El0100078 El0101069 El0102003 El0110069 El0111069 "
    "El0120069 El0200069 El0201069 El0210069 El0300069 El1000069 El1001069 "
    "El1010069 El1011069 El1020069 El1100069 El1101069 El1110069 El1200069 "
    "El2000069 El2001069 El2010069 El2100069 Em0000069 Em0001069 Em0002069 "
    "Em0003069 Em0010069 Em0011069 Em0012069 Em0020069 Em0021069 Em0030069 "
    "Em0100069 Em0101069 Em0102069 Em0110069 Em0111069 Em0120069 Em0200069 "
    "Em0201009 Em0210069 Em0300069 Em1000069 Em1001069 Em1002069 Em1010069 "
    "Em1100069 Em1110069 Em1200069 Em2000012 Em2010069 Em2100069 En0000072 "
    "En0001069 En0002031 En0003069 En0010059 En0011069 En0012069 En0020069 "
    "En0021069 En0100015 En0101069 En0102080 En0110069 En0111069 En0120069 "
    "En0200069 En0201069 En0210069 En0300069 En1000069 En1001069 En1002016 "
    "En1010069 En1011069 En1020069 En1100069 En1101069 En1110069 En1200069 "
    "En2000069 En2001069 En2010069 En2100069 En3000075 Eo0000069 Eo0001069 "
    "Eo0002069 Eo0003069 Eo0010069 Eo0011069 Eo0012069 Eo0020069 Eo0021069 "
    "Eo0030069 Eo0100069 Eo0101069 Eo0102069 Eo0110069 Eo0111069 Eo0120069 "
    "Eo0200069 Eo0201019 Eo0210069 Eo0300069 Eo1000069 Eo1001069 Eo1002069 "
    "Eo1010069 Eo1100069 Eo1101065 Eo1110069 Eo1200069 Eo2000036 Eo2010069 "
    "Eo2100069 Eo3000067 Ep0001069 Ep0002025 Ep0003069 Ep0010075 Ep0011069 "
    "Ep0012069 Ep0020069 Ep0021069 Ep0100033 Ep0101069 Ep0102015 Ep0110069 "
    "Ep0111069 Ep0120069 Ep0200069 Ep0201069 Ep0210069 Ep0300069 Ep1000069 "
    "Ep1001069 Ep1002023 Ep1010069 Ep1011069 Ep1020069 Ep1100069 Ep1101069 "
    "Ep1110069 Ep1200069 Ep2000069 Ep2001069 Ep2010069 Ep2100069 Ep3000042 "
    "Eq0000069 Eq0001069 Eq0002069 Eq0003069 Eq0010069 Eq0011069 Eq0012069 "
    "Eq0020069 Eq0021069 Eq0030069 Eq0100069 Eq0101069 Eq0102069 Eq0110069 "
    "Eq0111069 Eq0120069 Eq0200069 Eq0210069 Eq0300069 Eq1000069 Eq1001069 "
    "Eq1002069 Eq1010069 Eq1100069 Eq1110069 Eq1200069 Eq2000001 Eq2010069 "
    "Eq2100069 Er0000042 Er0001069 Er0002057 Er0003069 Er0010032 Er0011069 "
    "Er0012069 Er0020069 Er0021069 Er0100014 Er0101069 Er0110069 Er0111069 "
    "Er0120069 Er0200069 Er0201069 Er0210069 Er0300069 Er1000069 Er1001069 "
    "Er1010069 Er1011069 Er1020069 Er1100069 Er1101069 Er1110069 Er1200069 "
    "Er2000069 Er2001069 Er2010069 Er2100069 Es0000069 Es0001069 Es0002069 "
    "Es0003069 Es0010069 Es0011069 Es0012069 Es0020069 Es0021069 Es0030069 "
    "Es0100069 Es0101069 Es0102069 Es0110069 Es0111069 Es0120069 Es0200069 "
    "Es0210069 Es0300069 Es1000069 Es1001069 Es1002069 Es1010069 Es1100069 "
    "Es1110069 Es1200069 Es2010069 Es2100069 Et0000044 Et0001069 Et0003069 "
    "Et0010025 Et0011069 Et0012069 Et0020051 Et0021051 Et0100052 Et0101051 "
    "Et0110051 Et0111051 Et0120051 Et0200051 Et0201051 Et0210051 Et0300051 "
    "Et1000051 Et1001051 Et1010051 Et1011051 Et1020051 Et1100051 Et1101051 "
    "Et1110051 Et1200051 Et2000051 Et2001051 Et2010051 Et2100051 Eu0000051 "
    "Eu0001051 Eu0002051 Eu0003051 Eu0010051 Eu0011051 Eu0012051 Eu0020051 "
    "Eu0021051 Eu0030051 Eu0100051 Eu0101051 Eu0102051 Eu0110051 Eu0111051 "
    "Eu0120051 Eu0200051 Eu0201008 Eu0210051 Eu0300051 Eu1000051 Eu1001051 "
    "Eu1002051 Eu1010051 Eu1100051 Eu1101019 Eu1110051 Eu1200051 Eu2000049 "
    "Eu2001003 Eu2010051 Eu2100051 Eu3000031 Ev0000036 Ev0001051 Ev0002022 "
    "Ev0003051 Ev0010070 Ev0011051 Ev0012051 Ev0020051 Ev0021051 Ev0100073 "
    "Ev0101051 Ev0102031 Ev0110051 Ev0111051 Ev0120051 Ev0200051 Ev0201051 "
    "Ev0210051 Ev0300051 Ev1000051 Ev1001051 Ev1010051 Ev1011051 Ev1020051 "
    "Ev1100051 Ev1101051 Ev1110051 Ev1200051 Ev2000051 Ev2001051 Ev2010051 "
    "Ev2100051 Ev3000019 Ew0000051 Ew0001051 Ew0002051 Ew0003051 Ew0010016 "
    "Ew0011016 Ew0012016 Ew0020016 Ew0021016 Ew0030016 Ew0100016 Ew0101016 "
    "Ew0102016 Ew0110016 Ew0111016 Ew0120016 Ew0200036 Ew0210036 Ew0300036 "
    "Ew1000057 Ew1001057 Ew1002057 Ew1010014 Ew1100078 Ew1110078 Ew1200078 "
    "Ew2010078 Ew2100078 Ex0000054 Ex0001078 Ex0002037 Ex0003078 Ex0010015 "
    "Ex0011078 Ex0012078 Ex0020078 Ex0021078 Ex0100076 Ex0101078 Ex0102067 "
    "Ex0110078 Ex0111078 Ex0120078 Ex0200078 Ex0201078 Ex0210078 Ex0300078 "
    "Ex1000078 Ex1001078 Ex1002005 Ex1010078 Ex1011078 Ex1020078 Ex1100078 "
    "Ex1101078 Ex1110078 Ex1200078 Ex2000078 Ex2001078 Ex2010078 Ex2100078 "
)

# =============================================================================
# Part A: the certificates
# =============================================================================
# (name, l, n, mode, r, a, b); the target depends on l and on the mode, the modulus is 3**n,
# the class is w == r (mod 3), i.e. k == 2 (r=0), k == 0 (r=1), k == 4 (r=2) modulo 6.
TABLE = [
    ('L7_R0', 7, 4, 'lin', 0, None, None), ('L7_R1', 7, 4, 'lin', 1, None, None), ('L7_R2', 7, 3, 'lin', 2, None, None),
    ('L7_R2M', 7, 4, 'lin7k4', 2, None, None),
    ('L13_R0', 13, 4, 'lin', 0, None, None), ('L13_R1', 13, 4, 'lin', 1, None, None), ('L13_R2', 13, 3, 'lin', 2, None, None),
    ('L19_R0', 19, 5, 'lin', 0, None, None), ('L19_R1', 19, 5, 'lin', 1, None, None), ('L19_R2', 19, 4, 'lin', 2, None, None),
    ('L5_R0', 5, 4, 'sq', 0, None, None), ('L5_R1', 5, 4, 'sq', 1, None, None),
    ('L5_R2', 5, 4, 'quad', 2, [51, 51, 51, 18, 24, 21], [51, 51, 51, 18, 45, 0]),
    ('L11_R0', 11, 4, 'sq', 0, None, None), ('L11_R1', 11, 4, 'sq', 1, None, None),
    ('L11_R2', 11, 4, 'quad', 2, [70, 70, 70, 56, 11, 29], [70, 70, 70, 56, 38, 74]),
    ('L17_R0', 17, 5, 'sq', 0, None, None), ('L17_R1', 17, 5, 'sq', 1, None, None),
    ('L19_R2M', 19, 5, 'lin19k4', 2, None, None),
]

def controle_taylor(R):
    """the formula of coord_kappa reproduces the direct substitution, modulo 3**n"""
    N = R.N
    essais = [(4, 3, 6, 7), (7, 0, 3, 1), (1, 6, 0, 4), (N - 2, 3, N - 3, 1), (10, 9, 3, N - 8), (25, N - 3, 9, 13)]
    for k in essais:
        cf = R.coord_kappa(k)
        for i in range(7):
            for j in range(7):
                direct = image_monome(i + j, i, k[0], k[1], k[2], k[3], N)
                formule = [0] * (i + j + 1)
                for (dl, A, B), v in cf.items():
                    e = i + dl
                    if 0 <= e <= i + j:
                        formule[e] += v * comb(i, A) * comb(j, B)
                if any((direct[e] - formule[e]) % N for e in range(i + j + 1)):
                    return False
    return True

def consequences_quad(l, n, a, b):
    """for even w == 2 (mod 3), Lam_l acts by lam = l**w; we check b(lam) == 0 (mod 3**n)
    and a(lam) == 0 (mod 9): then every eigenvalue t satisfies t (t + a) == 0 (mod 3**n), hence 9 | t"""
    N = 3 ** n
    for t in range(27):
        lam = pow(l, 2 + 6 * t, N)
        av = sum(a[i] * pow(lam, i, N) for i in range(len(a))) % N
        bv = sum(b[i] * pow(lam, i, N) for i in range(len(b))) % N
        if bv != 0 or av % 9 != 0:
            return False
    return True

def partie_A():
    dire('')
    dire('Part A: certificates (criterion of Lemma 7), nineteen in all')
    anneaux = {}
    ok_tout = True
    restes = {}
    for nom, l, n, mode, r, a, b in TABLE:
        t1 = time.time()
        if n not in anneaux:
            anneaux[n] = Anneau(n)
            okt = controle_taylor(anneaux[n])
            dire('  ring modulo %d: expansion of sigma_kappa agrees with the substitution: %s' % (3 ** n, 'yes' if okt else 'NO'))
            ok_tout = ok_tout and okt
        R = anneaux[n]
        texte = globals()['CERT_' + nom]
        zeta, nt = R.zeta(texte)
        Xi = cible(R, l, mode, a, b)
        reste = somme(R.N, (1, Xi), (-1, zeta))
        ok, nb = R.critere_nul(reste, r)
        temoin = not R.critere_nul(Xi, r)[0]
        extra = ''
        if mode == 'quad':
            okq = consequences_quad(l, n, a, b)
            ok = ok and okq
            extra = ' ; b(lam) == 0 and a(lam) == 0 mod 9 on the class: %s' % ('yes' if okq else 'NO')
        restes[nom] = (reste, r, n, l, mode)
        dire('  %-7s l=%2d  k == %d (mod 6)  mode %-4s modulo %3d : %4d terms, remainder of %4d matrices ; criterion: %s ; witness: %s%s  (%.1f s)'
             % (nom, l, {0: 2, 1: 0, 2: 4}[r], mode, 3 ** n, nt, len(reste), 'VERIFIED' if ok else 'FAILED', 'yes' if temoin else 'NO', extra, time.time() - t1))
        ok_tout = ok_tout and ok and temoin
    return ok_tout, restes

# =============================================================================
# Part B: direct action of the remainder on the forms of degree w
# =============================================================================
def action_directe(X, f, w, N):
    tot = [0] * (w + 1)
    for g, cg in X.items():
        a, b, c, d = g
        vp = [[1] + [0] * w]
        for m in range(1, w + 1):
            p = vp[-1]
            vp.append([(d * p[0]) % N] + [(b * p[e - 1] + d * p[e]) % N for e in range(1, w + 1)])
        Rr = [f[w] % N] + [0] * w
        for i in range(w - 1, -1, -1):
            V = vp[w - i]
            fi = f[i]
            Rr = [(c * Rr[0] + fi * V[0]) % N] + [(a * Rr[e - 1] + c * Rr[e] + fi * V[e]) % N for e in range(1, w + 1)]
        for e in range(w + 1):
            tot[e] = (tot[e] + cg * Rr[e]) % N
    return tot

def partie_B(restes):
    dire('')
    dire('Part B: direct check, action of the remainders on the forms of degree w <= %d' % W_B_MAX)
    ok_tout = True
    for nom, (reste, r, n, l, mode) in restes.items():
        N = 3 ** n
        degs = [w for w in range(2, W_B_MAX + 1, 2) if w % 3 == r]
        temoins = [w for w in range(W_B_MAX - 5, W_B_MAX + 1) if w % 2 == 0 and w % 3 != r]
        res = []
        for w in degs + temoins:
            f = [(7 * i * i + 3 * i + 5) % N for i in range(w + 1)]
            nul = not any(action_directe(reste, f, w, N))
            if w % 3 == r:
                ok_tout = ok_tout and nul
                res.append('w=%d:%s' % (w, 'yes' if nul else 'NO'))
            else:
                res.append('w=%d(out of class):%s' % (w, 'no' if not nul else 'YES?'))
        dire('  %-7s modulo %3d : ' % (nom, N) + ' '.join(res))
        if time.time() - T0 > BUDGET:
            dire('  budget reached')
            return ok_tout
    return ok_tout

# =============================================================================
# Part C: statement (O) weight by weight, at the level of eigenvalues
# =============================================================================
def lignes_relations(w):
    rows = []
    for j in range(w + 1):
        imS = image_monome(w, j, 0, -1, 1, 0)
        imU = image_monome(w, j, 1, -1, 1, 0)
        imU2 = image_monome(w, j, 0, -1, 1, -1)
        imE = image_monome(w, j, -1, 0, 0, 1)
        rS = imS[:]
        rS[j] += 1
        rU = [imU[i] + imU2[i] for i in range(w + 1)]
        rU[j] += 1
        rE = imE[:]
        rE[j] += 1
        rows += [rS, rU, rE]
    return rows

def noyau_rationnel(rows, n):
    M = [[Fraction(x) for x in r] for r in rows if any(r)]
    piv_cols = []
    r = 0
    for c in range(n):
        p = None
        for i in range(r, len(M)):
            if M[i][c] != 0:
                p = i
                break
        if p is None:
            continue
        M[r], M[p] = M[p], M[r]
        inv = 1 / M[r][c]
        M[r] = [x * inv for x in M[r]]
        for i in range(len(M)):
            if i != r and M[i][c] != 0:
                f = M[i][c]
                M[i] = [M[i][k] - f * M[r][k] for k in range(n)]
        piv_cols.append(c)
        r += 1
        if r == len(M):
            break
    libres = [c for c in range(n) if c not in piv_cols]
    base = []
    for fcol in libres:
        v = [Fraction(0)] * n
        v[fcol] = Fraction(1)
        for i, pc in enumerate(piv_cols):
            v[pc] = -M[i][fcol]
        den = 1
        for x in v:
            den = den * x.denominator // gcd(den, x.denominator)
        vi = [int(x * den) for x in v]
        g = 0
        for x in vi:
            g = gcd(g, x)
        base.append([x // g for x in vi])
    return base

def dependance_mod3(base):
    d = len(base)
    n = len(base[0])
    M = [[base[i][k] % 3 for k in range(n)] + [1 if t == i else 0 for t in range(d)] for i in range(d)]
    r = 0
    for c in range(n):
        p = None
        for i in range(r, d):
            if M[i][c] % 3:
                p = i
                break
        if p is None:
            continue
        M[r], M[p] = M[p], M[r]
        inv = 1 if M[r][c] == 1 else 2
        M[r] = [(x * inv) % 3 for x in M[r]]
        for i in range(d):
            if i != r and M[i][c] % 3:
                f = M[i][c]
                M[i] = [(M[i][k] - f * M[r][k]) % 3 for k in range(n + d)]
        r += 1
    for i in range(r, d):
        if all(M[i][k] % 3 == 0 for k in range(n)):
            return M[i][n:]
    return None

def sature_en_3(base):
    base = [b[:] for b in base]
    while True:
        c = dependance_mod3(base)
        if c is None:
            return base
        i0 = next(i for i in range(len(c)) if c[i] % 3)
        v = [sum(c[i] * base[i][k] for i in range(len(base))) for k in range(len(base[0]))]
        base[i0] = [x // 3 for x in v]

def reseau_hatada(w):
    return sature_en_3(noyau_rationnel(lignes_relations(w), w + 1))

def matrice_Tn(w, n):
    """rows: m_l(T_n P) = sum_i Mt[l][i] m_i"""
    Mt = [[0] * (w + 1) for _ in range(w + 1)]
    for (a, b, c, d) in manin(n):
        for l in range(w + 1):
            im = image_monome(w, l, a, b, c, d)
            for i, x in enumerate(im):
                if x:
                    Mt[l][i] += x
    return Mt

def coordonnees(base, vecs):
    """express each vector of vecs (in the Z-module spanned by base) in coordinates on base"""
    d = len(base)
    n = len(base[0])
    # choose d columns where the base is invertible (rational elimination)
    M = [[Fraction(base[i][k]) for k in range(n)] for i in range(d)]
    piv = []
    r = 0
    for c in range(n):
        p = None
        for i in range(r, d):
            if M[i][c] != 0:
                p = i
                break
        if p is None:
            continue
        M[r], M[p] = M[p], M[r]
        inv = 1 / M[r][c]
        M[r] = [x * inv for x in M[r]]
        for i in range(d):
            if i != r and M[i][c] != 0:
                f = M[i][c]
                M[i] = [M[i][k] - f * M[r][k] for k in range(n)]
        piv.append(c)
        r += 1
        if r == d:
            break
    # solve sum_i x_i base[i][piv] = vec[piv]
    A = [[Fraction(base[i][c]) for i in range(d)] for c in piv]   # d x d
    out = []
    for v in vecs:
        rhs = [Fraction(v[c]) for c in piv]
        Mx = [A[i][:] + [rhs[i]] for i in range(d)]
        for c in range(d):
            p = next(i for i in range(c, d) if Mx[i][c] != 0)
            Mx[c], Mx[p] = Mx[p], Mx[c]
            inv = 1 / Mx[c][c]
            Mx[c] = [x * inv for x in Mx[c]]
            for i in range(d):
                if i != c and Mx[i][c] != 0:
                    f = Mx[i][c]
                    Mx[i] = [Mx[i][k] - f * Mx[c][k] for k in range(d + 1)]
        x = [Mx[i][d] for i in range(d)]
        for xi in x:
            if xi.denominator % 3 == 0:
                raise ValueError('coordinate not 3-integral')
        # full check (the base is saturated at 3 only: coordinates in Z_(3))
        for k in range(n):
            if sum(x[i] * base[i][k] for i in range(d)) != v[k]:
                raise ValueError('vector outside the lattice')
        out.append(x)
    return out

def polcar(A):
    """characteristic polynomial (Faddeev-LeVerrier), coefficients c_0..c_d in Z_(3), monic"""
    d = len(A)
    Mk = [[Fraction(0)] * d for _ in range(d)]
    c = [Fraction(0)] * (d + 1)
    c[d] = Fraction(1)
    for k in range(1, d + 1):
        # M_k = A M_{k-1} + c_{d-k+1} I
        Mk = [[sum(A[i][t] * Mk[t][j] for t in range(d)) + (c[d - k + 1] if i == j else 0) for j in range(d)] for i in range(d)]
        tr = sum(sum(A[i][t] * Mk[t][i] for t in range(d)) for i in range(d))
        c[d - k] = -tr / k
    return c

def v3frac(x):
    x = Fraction(x)
    if x == 0:
        return 10 ** 9
    return v3(x.numerator) - v3(x.denominator)

def sigma_k(n, e):
    return sum(d ** e for d in range(1, n + 1) if n % d == 0)

def pentes_ok(c, s, seuil):
    """all roots of P(x) = sum c_i x**i satisfy v3(root - s) >= threshold:
    Newton polygon of Q(x) = P(x + s): v3(q_i) >= threshold (d - i)"""
    d = len(c) - 1
    q = [Fraction(0)] * (d + 1)
    for i in range(d + 1):
        for j in range(i + 1):
            q[j] += c[i] * comb(i, j) * s ** (i - j)
    for i in range(d):
        if q[i] != 0 and v3frac(q[i]) < seuil * (d - i):
            return False
    return True

def partie_C():
    dire('')
    dire('Part C: a_n == sigma_{k-1}(n) (mod 81) for n == 1 (mod 3), n <= k (Sturm bound), 12 <= k <= %d' % KMAX_O)
    echecs = 0
    for k in range(12, KMAX_O + 1, 2):
        if k == 14:
            continue
        t1 = time.time()
        w = k - 2
        base = reseau_hatada(w)
        d = len(base)
        ok = True
        pire = None
        for n in range(4, k + 1, 3):
            Mt = matrice_Tn(w, n)
            images = [[sum(r[i] * m[i] for i in range(w + 1) if r[i] and m[i]) for r in Mt] for m in base]
            A = coordonnees(base, images)        # A[j] = coordinates of T_n(b_j): matrix (columns)
            At = [[A[j][i] for j in range(d)] for i in range(d)]
            c = polcar(At)
            s = sigma_k(n, k - 1)
            if not pentes_ok(c, s, 4):
                ok = False
                pire = n
            if time.time() - T0 > BUDGET:
                dire('  budget reached during k = %d' % k)
                return echecs == 0
        if not ok:
            echecs += 1
        dire('  k=%3d d=%2d  n == 1 (mod 3), 4 <= n <= %3d : %s%s  (%.1f s)' % (k, d, k, 'ok' if ok else 'FAILED', '' if ok else ' (n=%d)' % pire, time.time() - t1))
    dire('  failing weights: %d (expected: 0)' % echecs)
    return echecs == 0


# =============================================================================
# Part D: laws (P), (R), (S) on the lattice L_k, at the level of eigenvalues
# =============================================================================
def mprod(A, B):
    d = len(A)
    return [[sum(A[i][t] * B[t][j] for t in range(d)) for j in range(d)] for i in range(d)]

def mcomb(*termes):
    """sum of c * M (c an integer or Fraction, M a matrix); a term (c, None) stands for c * I"""
    d = None
    for c, M in termes:
        if M is not None:
            d = len(M)
    out = [[Fraction(0)] * d for _ in range(d)]
    for c, M in termes:
        for i in range(d):
            for j in range(d):
                out[i][j] += c * (M[i][j] if M is not None else (1 if i == j else 0))
    return out

def matrice_sur_reseau(base, w, n):
    Mt = matrice_Tn(w, n)
    images = [[sum(r[i] * m[i] for i in range(w + 1) if r[i] and m[i]) for r in Mt] for m in base]
    A = coordonnees(base, images)
    d = len(base)
    return [[A[j][i] for j in range(d)] for i in range(d)]

def cube_mod(l):
    return pow(3, (l - 1) // 3, l) == 1

def u_de(m):
    """u = 0 if m == 1 (mod 9), 1 otherwise (for m == 1 (mod 3))"""
    return 0 if m % 9 == 1 else 1

def ut_de(l):
    return {2: -1, 5: 1, 8: 0}[l % 9]

LISTE_D = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 73]

def partie_D():
    dire('')
    dire('Part D: laws (P) modulo 243, (R) modulo 729, (S) modulo 243, on L_k, 12 <= k <= %d' % KMAX_D)
    echecs = 0
    temoins = 0
    for k in range(12, KMAX_D + 1, 2):
        if k == 14:
            continue
        t1 = time.time()
        w = k - 2
        base = reseau_hatada(w)
        s = lambda l: 1 + l ** (k - 1)
        A = {2: matrice_sur_reseau(base, w, 2)}
        for l in LISTE_D:
            A[l] = matrice_sur_reseau(base, w, l)
        Z = mcomb((1, mprod(A[2], A[2])), (-s(2) ** 2, None))           # T_2**2 - s_2**2
        ok = True
        for l in LISTE_D:
            if l % 3 == 1:
                X = mcomb((1, A[l]), (-s(l), None), (-u_de(l), Z))
                X0 = mcomb((1, A[l]), (-s(l), None))
                if u_de(l) and not pentes_ok(polcar(X0), 0, 5):
                    temoins += 1
            else:
                X = mcomb((1, mprod(A[l], A[l])), (-s(l) ** 2, None), (-u_de(l * l), Z))
            if not pentes_ok(polcar(X), 0, 5):
                ok = False
            if (l % 9 == 1 and cube_mod(l)) or l % 9 == 8:            # law (R)
                Y = mcomb((1, A[l]), (-s(l), None)) if l % 9 == 1 else mcomb((1, mprod(A[l], A[l])), (-s(l) ** 2, None))
                if not pentes_ok(polcar(Y), 0, 6):
                    ok = False
        P2 = [2] + [l for l in LISTE_D if l % 3 == 2]
        for i, l in enumerate(P2):
            for m in P2[i:]:
                X = mcomb((1, mprod(A[l], A[m])), (-s(l) * s(m), None), (-ut_de(l) * ut_de(m), Z))
                if not pentes_ok(polcar(X), 0, 5):
                    ok = False
        if not ok:
            echecs += 1
        dire('  k=%3d d=%2d  (P), (R), (S) for l in %s : %s  (%.1f s)' % (k, len(base), LISTE_D, 'ok' if ok else 'FAILED', time.time() - t1))
        if time.time() - T0 > BUDGET:
            dire('  budget reached during k = %d' % k)
            break
    dire('  failing weights: %d (expected: 0) ; cases where the correction term is necessary: %d (expected: > 0)' % (echecs, temoins))
    return echecs == 0 and temoins > 0

# =============================================================================
# Self-test and summary
# =============================================================================
def auto_test():
    if pow(2, 11) != 2048 or comb(10, 3) != 120 or v3(252) != 2 or len(REPS24) != 24:
        return False
    base = reseau_hatada(10)
    if len(base) != 1:
        return False
    m = base[0]
    if [m[j] for j in range(1, 10, 2)] not in ([48, -25, 20, -25, 48], [-48, 25, -20, 25, -48]):
        return False
    A = coordonnees(base, [[sum(r[i] * m[i] for i in range(11)) for r in matrice_Tn(10, 2)]])
    if A[0][0] != -24:
        return False
    A7 = coordonnees(base, [[sum(r[i] * m[i] for i in range(11)) for r in matrice_Tn(10, 7)]])
    if A7[0][0] != -16744:                      # tau(7)
        return False
    return len(manin(2)) == 4 and len(manin(3)) == 7 and sigma_k(6, 1) == 12

dire('=' * 76)
dire('VERIF_EISENSTEIN: Eisenstein congruences modulo 81, 243 and 729 in level 1')
dire('Budget %.0f s ; Part B: w <= %d ; Part C: k <= %d' % (BUDGET, W_B_MAX, KMAX_O))
dire('=' * 76)
if not auto_test():
    dire('SELF-TEST FAILED: stop (non-conforming environment).')
    sys.exit(1)
dire('Self-test: OK (period of Delta, tau(2) = -24, tau(7) = -16744, Manin sets).')
rA, restes = partie_A()
rB = partie_B(restes) if PARTIE_B else True
rC = partie_C() if PARTIE_C else True
rD = partie_D() if PARTIE_D else True
dire('')
dire('SUMMARY: Part A (certificates) %s, Part B (direct check) %s, Part C (Sturm, k <= %d) %s, Part D (laws P, R, S, k <= %d) %s'
     % ('OK' if rA else 'FAILED', 'OK' if rB else 'FAILED', KMAX_O, 'OK' if rC else 'FAILED', KMAX_D, 'OK' if rD else 'FAILED'))
dire('Total time: %.1f s' % (time.time() - T0))