#include "bits/stdc++.h" using namespace std; //諸機能 #pragma region MACRO #define ANSWER(x) cerr << "answer: "; cout << (x) << endl #define DOUBLE_ANSWER(x) cerr << "answer: "; cout << setprecision(10) << (double)(x) << endl #define REP(i,a,n) for(int i=(a); i<(int)(n); i++) #define RREP(i,a,n) for(int i=(int)(n); i>= a; i--) #define rep(i,n) REP(i,0,n) #define rrep(i,n) RREP(i,0,n) #define ALL(a) begin((a)),end((a)) #define FILL(a,n) for(auto &hoge : (a)) hoge = (n) #define mp make_pair #define EXIST(container, n) ((container).find((n)) != (container).end()) #define STOI(s,i,l) stoi(SUBSTR(s,i,l)) #define SUBSTR(s,i,l) string((s), (i), (l)) #define NPI_TO_RAD(x) (180.0*x/PI) #define RAD_TO_NPI(x) (PI/180.0*x) #pragma endregion //デバッグなどの支援 #pragma region CODING_SUPPORT #define DEBUG1(var0) { std::cerr << ( #var0 ) << "=" << ( var0 ) << endl; } #define DEBUG2(var0, var1) { std::cerr << ( #var0 ) << "=" << ( var0 ) << ", "; DEBUG1(var1); } #define DEBUG3(var0, var1, var2) { std::cerr << ( #var0 ) << "=" << ( var0 ) << ", "; DEBUG2(var1, var2); } #define DEBUG4(var0, var1, var2, var3) { std::cerr << ( #var0 ) << "=" << ( var0 ) << ", "; DEBUG3(var1, var2, var3); } #ifndef _DEBUG //デバッグでないなら、計算時間短縮のためにエラー出力を無効化 #define DEBUG1{} #define DEBUG2{} #define DEBUG3{} #define DEBUG4{} #endif //typedef(書き換える、書き足す可能性ある) #pragma region TYPE_DEF typedef long long ll; typedef pair pii; typedef pair pss; typedef pairpis; typedef pairpsi; typedef vector vs; typedef vector vi; #pragma endregion //諸々の定数(書き換える可能性ある) #pragma region CONST_VAL #define PI (2*acos(0.0)) #define EPS (1e-9) #define MOD (int)(1e9 + 7) #pragma endregion struct Matrix { vector > v, w; Matrix() {} Matrix(int n, int m) : v(n, vector(m)) { } inline int height() const { return (int)v.size(); } inline int width() const { return (int)v[0].size(); } inline double& at(int i, int j) { return v[i][j]; } inline const double& at(int i, int j) const { return v[i][j]; } static Matrix identity(int n) { Matrix A(n, n); rep(i, n) A.at(i, i) = 1; return A; } inline static Matrix identity(const Matrix& A) { return identity(A.height()); } Matrix& operator*=(const Matrix& B) { int n = height(), m = B.width(), p = B.height(); assert(p == width()); w.assign(n, vector(m, 0)); rep(i, n) { rep(j, m) { double x = 0; rep(k, p) { x += at(i, k) * B.at(k, j); } w[i][j] = x; } } v.swap(w); return *this; } }; Matrix operator^(const Matrix& t, ll k) { Matrix A = t, B = Matrix::identity(t); while (k) { if (k & 1) B *= A; A *= A; k >>= 1; } return B; } int main() { ll n; cin >> n; Matrix abase(6, 6); Matrix bbase(7, 7); Matrix initaa(6, 1); Matrix initab(7, 1); initab.at(6, 0) = 1; rep(i, 6) { initaa.at(i, 0) = 1; abase.at(0, i) = 1.0 / 6; bbase.at(0, i) = 1.0 / 6; } initaa.at(0, 0) = 0; rep(i, 5) { abase.at(1 + i, i) = 1; bbase.at(i+1,i) = 1; } bbase.at(0, 6) = 1; bbase.at(6,6) = 1; rep(count, n) { double k; cin >> k; Matrix tmpa = abase ^ k; Matrix tmpb = bbase ^ k; double a0 = 0; rep(i, 6) { a0 += tmpa.at(0, i) * initaa.at(i, 0); } double b0 = 0; rep(i, 7) { b0 += tmpb.at(0, i) * initab.at(i, 0); } DEBUG1(a0); DEBUG1(b0); cout << setprecision(13) << b0 / ( 1 - a0 ) << endl; } return 0; }