1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 #include #define FOR(i, a, b) for (int i=(a); i<(b); i++) #define PPC(x) __builtin_popcount((x)) #define ALL(x) (x).begin(), (x).end() #define pb push_back #define st first #define nd second using namespace std; const int maxN = 10101, mod = 1000000007; inline void addMod(long long& a, long long b) { a = (a + b) % mod; } inline void multMod(long long& a, long long b) { a = a * b % mod; } long long qpow(long long a, long long b) { long long res0 = 1; for (; b!=0; b>>=1) { if (b & 1) multMod(res0, a); multMod(a, a); } return res0; } int nk[maxN][maxN], pref[maxN][maxN]; int n; char in[3][maxN]; int same[3][3], r[3], same2, lon[3]; void compNk() { nk[0][0] = pref[0][1] = 1ll; FOR(i, 1, n+1) { nk[i][0] = 1ll; FOR(j, 1, i+2) { nk[i][j] = (nk[i-1][j-1] + nk[i-1][j]) % mod; pref[i][j] = (pref[i][j-1] + nk[i][j-1]) % mod; } } } inline long long sum(int i, int j, int k) { return k < j ? 0ll : (long long)pref[i][k+1] + mod - pref[i][j]; } long long licz1(int i) { return sum(n, 0, r[i]) % mod; } long long licz2(int i, int j) { int s = same[i][j], s2 = n - s; long long res = 0; FOR(d, 0, min({s, r[i], r[j]}) + 1) { int a = max(0, s2+d-r[j]); int b = min(s2, r[i]-d); addMod(res, sum(s2, a, b) * nk[s][d]); } return res; } long long licz3() { int s = same2; int r0 = r[0], r1 = r[1], r2 = r[2]; int lon0 = lon[0], lon1 = lon[1], lon2 = lon[2]; long long res = 0; //printf("[%d %d %d %d]\n", s, lon0, lon1, lon2); assert(s + lon0 + lon1 + lon2 == n); FOR(d, 0, min({s, r0, r1, r2}) + 1) { long long prod0 = nk[s][d]; int a0 = max(0, d+lon0-min(r1, r2)); int b0 = min(lon0, r0-d); FOR(e0, a0, b0+1) { long long prod1 = prod0 * nk[lon0][e0] % mod; int f0 = lon0-e0; int a1 = max({0, d+e0+lon1-r0, d+f0+lon1-r2}); int b1 = min(lon1, r1-d-f0); long long x = 0ll; FOR(e1, a1, b1+1) { int f1 = lon1-e1; int a2 = max({0, d+e0+f1-r0+lon2, d+e1+f0-r1+lon2}); int b2 = min(lon2, r2-d-f0-f1); addMod(x, sum(lon2, a2, b2) * nk[lon1][e1]); } addMod(res, prod1 * x); } } return res; } int main() { scanf ("%d", &n); FOR(s, 0, 3) scanf ("%d%s", r+s, &in[s][0]); compNk(); FOR(i, 0, n) { FOR(a, 0, 3) FOR(b, a+1, 3) if (in[a][i] == in[b][i]) same[a][b]++; if (in[0][i] == in[1][i] and in[1][i] == in[2][i]) same2++; else { if (in[0][i] == in[1][i]) lon[2]++; if (in[0][i] == in[2][i]) lon[1]++; if (in[1][i] == in[2][i]) lon[0]++; } } long long res = licz3(); FOR(i, 0, 3) { addMod(res, licz1(i)); FOR(j, i+1, 3) addMod(res, mod-licz2(i, j)); } printf("%lld\n", res); return 0; }