#include #include #include using namespace std; constexpr int mod = 1e9 + 7; struct Modint { int n; Modint(int n = 0) : n(n) {} }; Modint operator+(Modint a, Modint b) { return Modint((a.n += b.n) >= mod ? a.n - mod : a.n); } Modint operator-(Modint a, Modint b) { return Modint((a.n -= b.n) < 0 ? a.n + mod : a.n); } Modint operator*(Modint a, Modint b) { return Modint(1LL * a.n * b.n % mod); } Modint &operator+=(Modint &a, Modint b) { return a = a + b; } Modint &operator-=(Modint &a, Modint b) { return a = a - b; } Modint &operator*=(Modint &a, Modint b) { return a = a * b; } Modint modinv(Modint n) { if (n.n == 1) return 1; return modinv(mod % n.n) * (mod - mod / n.n); } Modint operator/(Modint a, Modint b) { return a * modinv(b); } // ref: https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm std::vector berlekamp_massey(std::vector s) { using K = Modint; const int N = s.size(); std::vector C(N); std::vector B(N); C[0] = 1; B[0] = 1; int L = 0; int m = 1; K b = 1; for (int n = 0; n < N; n++) { K d = s[n]; for (int i = 1; i <= L; i++) d += C[i] * s[n - i]; if (d.n == 0) { m++; } else if (2 * L <= n) { auto T = C; for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * (d / b); L = n + 1 - L; B = T; b = d; m = 1; } else { for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * (d / b); m++; } } C.resize(L + 1); reverse(C.begin(), C.end()); return C; } vector poly_mod(vector a, const vector &m) { const int n = m.size(); for (int i = a.size() - 1; i >= m.size(); i--) { for (int j = 0; j < m.size(); j++) { a[i - n + j] += a[i] * m[j]; } } a.resize(m.size()); return a; } // a*b mod m(x) vector poly_mul(const vector &a, const vector &b, const vector &m) { vector ret(a.size() + b.size() - 1); for (int i = 0; i < a.size(); i++) { for (int j = 0; j < b.size(); j++) { ret[i + j] += a[i] * b[j]; } } return poly_mod(ret, m); } // x^n mod m(x) vector nth_power(long long n, const vector &m) { vector ret(1); vector x(2); ret[0] = x[1] = 1; while (n > 0) { if (n & 1) ret = poly_mul(ret, x, m); x = poly_mul(x, x, m); n /= 2; } return poly_mod(ret, m); } int main() { int c[10] = {0, 4, 4, 4, 6, 8, 8, 6, 8, 0}; vector> g = { /* 0 */ {0, 1, 2, 3, 4, 5, 7, 8}, /* 0 */ {0, 0, 0, 0, 0, 0, 0, 0}, /* 1 */ {1, 4, 5, 8, 9}, /* 1 */ {1, 1, 1, 1, 0}, /* 2 */ {2, 4, 7, 8, 9}, /* 2 */ {1, 1, 1, 1, 0}, /* 3 */ {3, 5, 7, 8, 9}, /* 3 */ {1, 1, 1, 1, 0}, /* 4 */ {1, 2, 4, 7, 8, 9}, /* 4 */ {1, 1, 2, 1, 2, 0}, /* 5 */ {5, 8}, /* 5 */ {2, 2}, /* 6 */ {1, 3, 6, 9}, /* 6 */ {1, 1, 2, 0}, /* 7 */ {2, 3, 4, 7, 8, 9}, /* 7 */ {1, 1, 1, 2, 2, 0}, /* 8 */ {1, 2, 3, 4, 6, 7, 8, 9}, /* 8 */ {1, 1, 1, 2, 2, 2, 3, 0}, /* 9 */ {9}, /* 9 */ {0}, }; // std::vector s = {" ", "o ", " o ", " o", "oo ", "o o", "o o", " oo", "ooo", " "}; // for (int i = 0; i < 10; i++) { // for (int j = 0; j < g[i * 2].size(); j++) { // int ii = g[i * 2][j]; // std::cout << s[i] << std::endl; // std::cout << s[ii] << std::endl; // std::cout << g[i * 2 + 1][j] << std::endl; // std::cout << std::endl; // } // } static Modint dp[55][10][1000]; dp[0][0][0] = 1; for (int i = 0; i < 50; i++) { for (int j = 0; j < 10; j++) { for (int k = 0; k < 950; k++) { for (int l = 0; l < g[j * 2].size(); l++) { int jj = g[j * 2][l]; dp[i + 1][jj][k + c[jj] - 2 * g[j * 2 + 1][l]] += dp[i][j][k]; } } } } std::vector a; for (int i = 1; i <= 50; i++) { Modint ret; for (int j = 0; j < 1000; j++) { ret += dp[i][9][j] * j; } a.push_back(ret); cerr << ret.n << endl; } vector m = berlekamp_massey(a); m.pop_back(); for (int i = 0; i < m.size(); i++) { m[i] *= mod - 1; } long long n; cin >> n; auto x = nth_power(n, m); Modint ans; for (int i = 0; i < x.size(); i++) { ans += x[i] * a[i]; } cout << ans.n << endl; }