#pragma GCC optimize("O3") #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize("Ofast") #pragma GCC optimize("inline") #pragma GCC optimize("-fgcse") #pragma GCC optimize("-fgcse-lm") #pragma GCC optimize("-fipa-sra") #pragma GCC optimize("-ftree-pre") #pragma GCC optimize("-ftree-vrp") #pragma GCC optimize("-fpeephole2") #pragma GCC optimize("-ffast-math") #pragma GCC optimize("-fsched-spec") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("-falign-jumps") #pragma GCC optimize("-falign-loops") #pragma GCC optimize("-falign-labels") #pragma GCC optimize("-fdevirtualize") #pragma GCC optimize("-fcaller-saves") #pragma GCC optimize("-fcrossjumping") #pragma GCC optimize("-fthread-jumps") #pragma GCC optimize("-funroll-loops") #pragma GCC optimize("-freorder-blocks") #pragma GCC optimize("-fschedule-insns") #pragma GCC optimize("inline-functions") #pragma GCC optimize("-ftree-tail-merge") #pragma GCC optimize("-fschedule-insns2") #pragma GCC optimize("-fstrict-aliasing") #pragma GCC optimize("-falign-functions") #pragma GCC optimize("-fcse-follow-jumps") #pragma GCC optimize("-fsched-interblock") #pragma GCC optimize("-fpartial-inlining") #pragma GCC optimize("no-stack-protector") #pragma GCC optimize("-freorder-functions") #pragma GCC optimize("-findirect-inlining") #pragma GCC optimize("-fhoist-adjacent-loads") #pragma GCC optimize("-frerun-cse-after-loop") #pragma GCC optimize("inline-small-functions") #pragma GCC optimize("-finline-small-functions") #pragma GCC optimize("-ftree-switch-conversion") #pragma GCC optimize("-foptimize-sibling-calls") #pragma GCC optimize("-fexpensive-optimizations") #pragma GCC optimize("inline-functions-called-once") #pragma GCC optimize("-fdelete-null-pointer-checks") #pragma GCC optimize("Ofast") //#pragma GCC target("avx,avx2,fma") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") //#pragma GCC optimization ("unroll-loops") #include using namespace std; long double dp[3001]; long double res[3001]; int main(void) { cin.tie(0); ios::sync_with_stdio(false); for(int n=1;n<=3000;n++) { double lo = 0; double hi = 5e4; for (int i = 0; i < 25; i++) { double mid = (lo + hi) / 2; dp[0] = 0; for (int j = 1; j <= n; j++) { dp[j] = 1; for (int k = 1; k <= 6; k++) { if (j - k >= 0) { dp[j] += (dp[j - k] / 6); } else { dp[j] += (mid / 6); } } } if (dp[n] > mid) { lo = mid; } else { hi = mid; } } res[n] = (lo + hi) / 2; } cout << fixed; cout.precision(16); int tc; cin >> tc; while(tc--) { long long int n; cin >> n; if(n<=3000) cout << res[n] << '\n'; else cout << n << ".666666666666667" << '\n'; } return 0; }