#include #include typedef std::vector matrix_base; typedef std::vector matrix; matrix mul(const matrix& a, const matrix& b) { assert(a[0].size() == b.size()); matrix ret(a.size(), matrix_base(b[0].size(), 0)); for (int i = 0; i < a.size(); i++) { for (int j = 0; j < b[0].size(); j++) { for (int k = 0; k < b.size(); k++) ret[i][j] += a[i][k] * b[k][j]; } } return ret; } matrix unit(int n) { matrix ret(n, matrix_base(n, 0)); for (int i = 0; i < n; i++) ret[i][i] = 1; return ret; } matrix power(const matrix& a, int b) { assert(a.size() == a[0].size()); matrix f = a, ret = unit(a.size()); while (b) { if (b & 1) ret = mul(ret, f); f = mul(f, f); b >>= 1; } return ret; } #include #include using namespace std; int Q, N; int main() { matrix s(7, matrix_base(1)); s[0][0] = 35077.0 / 20736; s[1][0] = 2653.0 / 1728; s[2][0] = 181.0 / 144; s[3][0] = 13.0 / 12; s[4][0] = 1.0; s[5][0] = 0.0; s[6][0] = 1.0; matrix e(7, matrix_base(7)); e[0] = matrix_base({ 1.0 / 12, 1.0 / 6, 1.0 / 4, 1.0 / 12, 1.0 / 4, 1.0 / 6, 1 }); e[1][0] = e[2][1] = e[3][2] = e[4][3] = e[5][4] = e[6][6] = 1.0; cin >> Q; while (Q--) { cin >> N; cout << fixed << setprecision(15) << mul(power(e, N), s)[5][0] << endl; } return 0; }