import std.stdio, std.array, std.string, std.conv, std.algorithm; import std.typecons, std.range, std.random, std.math, std.container; import std.numeric, std.bigint, core.bitop; int gaussianElimination(ref real[][] org_mat, ref real[] ret) { int N = org_mat.length.to!int; auto mat = new real[][](N, N+1); foreach (i; 0..N) foreach (j; 0..N+1) mat[i][j] = org_mat[i][j]; foreach (i; 0..N) { real maxval = 0; int maxrow = -1; foreach (j; i..N) if (abs(mat[j][i]) > maxval) maxval = abs(mat[j][i]), maxrow = j; if (maxval == 0) return -1; swap(mat[i], mat[maxrow]); foreach (j; i+1..N+1) mat[i][j] /= mat[i][i]; mat[i][i] = 1; foreach (j; 0..N) { if (j == i) continue; real mul = mat[j][i]; foreach (k; i..N+1) mat[j][k] -= mul*mat[i][k]; } } foreach (i; 0..N) ret[i] = mat[i][N]; return 0; } void solve(int K) { auto mat = new real[][](K, K+1); foreach (i; 0..K) foreach(j; 0..K+1) mat[i][j] = 0; foreach (i; 0..K) { foreach (j; 1..7) { auto next = (i+j > K) ? 0 : i+j; mat[i][K] -= 1.0L / 6; if (i + j != K) mat[i][next] += 1.0L/6; } mat[i][i] -= 1; } auto E = new real[](K); gaussianElimination(mat, E); writeln("%.9f", E[0]); } void main() { auto T = readln.chomp.to!int; while (T--) { auto N = readln.chomp.to!int; if (N <= 150) solve(N); else writefln("%.9f", N + 5.0L / 3); } }