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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 #include #include #include #include #include #include #include #include #include #include #include using namespace std; const int MAX_DIMENSION = 10001; const int MOD = 1e9 + 7; struct Ball { int dimension; std::string center; int radius; }; int cache[MAX_DIMENSION][MAX_DIMENSION]; int rows[MAX_DIMENSION][MAX_DIMENSION]; void Init(int N) { for (int n = 0; n <= N; n++) { for (int k = 0; k <= N; k++) { cache[n][k] = 0; rows[n][k] = 0; } } } int BinomialCoefficient(int n, int k) { if (n == k || k == 0) { return 1; } if(cache[n][k] > 0) { return cache[n][k]; } int v = BinomialCoefficient(n - 1, k - 1) + BinomialCoefficient(n - 1, k); v %= MOD; cache[n][k] = v; return v; } void ComputeRowSums(int N) { for (int n = 0; n <= N; n++) { rows[n][0] = 1; for (int k = 1; k <= n; k++) { rows[n][k] = rows[n][k - 1] + BinomialCoefficient(n, k); rows[n][k] %= MOD; } } } int GetSegmentSum(int n, int k1, int k2) { return (rows[n][k2] - (k1 == 0 ? 0 : rows[n][k1 - 1]) + MOD) % MOD; } int CountPointsInBall(const Ball& b) { long long points = 0; for (int r = 0; r <= b.radius; ++r) { points += BinomialCoefficient(b.dimension, r); } points %= MOD; return static_cast(points); } int CountPointsInTwoBallsIntersection(const Ball& b1, const Ball& b2) { int equal = 0; int different = 0; for (int i = 0; i < b1.dimension; i++) { if (b1.center[i] == b2.center[i]) { ++equal; } else { ++different; } } long long points = 0; for (int e = 0; e <= std::min(equal, std::min(b1.radius, b2.radius)); ++e) { int left = std::max(e + different - b2.radius, 0); int right = std::min(b1.radius - e, different); if (left > right) { continue; } long long v = (long long)BinomialCoefficient(equal, e) * GetSegmentSum(different, left, right); v %= MOD; points += v; } points %= MOD; return static_cast(points); } int CountPointsInThreeBallsIntersection(const Ball& b1, const Ball& b2, const Ball& b3) { int A = 0; int B = 0; int C = 0; int D = 0; for (int i = 0; i < b1.dimension; i++) { if (b1.center[i] == b2.center[i] && b2.center[i] == b3.center[i]) { A++; } else if (b1.center[i] == b3.center[i]) { B++; } else if (b2.center[i] == b3.center[i]) { C++; } else { D++; } } if (A + B == b1.dimension && b1.radius == b3.radius) { return CountPointsInTwoBallsIntersection(b1, b2); } if (A + C == b1.dimension && b2.radius == b3.radius) { return CountPointsInTwoBallsIntersection(b1, b2); } if (A + D == b1.dimension && b1.radius == b2.radius) { return CountPointsInTwoBallsIntersection(b1, b3); } int r = std::min(std::min(b1.radius, b2.radius), b3.radius); long long points = 0; for (int a = 0; a <= std::min(A, r); a++) { long long v = 0; for(int b = 0; b <= B && a + b <= b1.radius && a + b <= b3.radius && a + (B - b) <= b2.radius; b++) { long long w = 0; int X = a + b + C + D - b3.radius; int Y = b1.radius - a - b; int Z = b2.radius - a - B + b - C; for (int c = std::max(std::max((X - Z) / 2, X - D), 0); c <= std::min(Y, C); c++) { int left = std::max(X - c, 0); int right = std::min(std::min(Y - c, Z + c), D); if (left > right) { continue; } long long z = (long long)BinomialCoefficient(C, c) * GetSegmentSum(D, left, right); z %= MOD; w += z; } w %= MOD; w *= BinomialCoefficient(B, b); w %= MOD; v += w; } v %= MOD; v *= BinomialCoefficient(A, a); v %= MOD; points += v; } points %= MOD; return static_cast(points); } int main() { std::ios::sync_with_stdio(false); // Read input int n; std::cin >> n; Ball b1{.dimension = n}; std::cin >> b1.radius >> b1.center; Ball b2{.dimension = n}; std::cin >> b2.radius >> b2.center; Ball b3{.dimension = n}; std::cin >> b3.radius >> b3.center; // Preprocessing Init(n); ComputeRowSums(n); long long result = CountPointsInBall(b1) + CountPointsInBall(b2) + CountPointsInBall(b3) - CountPointsInTwoBallsIntersection(b1, b2) - CountPointsInTwoBallsIntersection(b2, b3) - CountPointsInTwoBallsIntersection(b1, b3) + CountPointsInThreeBallsIntersection(b1, b2, b3); std::cout << (((result % MOD) + MOD) % MOD) << '\n'; return 0; }