using System; using System.Linq; using System.Diagnostics; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Number = System.Int64; namespace Program { public class Solver { public void Solve() { const double p = 1.0 / 6; var T = sc.Integer(); var A = new double[7]; A[6] = 1; var B = new double[7]; for (int i = 0; i < 5; i++) B[i] = 1; var mat = new Matrix(7, 7); for (int i = 0; i < 5; i++) mat[i, i + 1] = 1.0; for (int i = 0; i < 6; i++) mat[5, i] = p; mat[5, 6] = mat[6, 6] = 1; Matrix.otaku(mat); for (int _ = 0; _ < T; _++) { var k = sc.Long(); var ret = Matrix.Pow(mat, k); var ggg = 0.0; for (int i = 0; i < 7; i++) ggg += ret[5, i] * A[i]; ret = Matrix.Pow(mat, k); var fff = 0.0; for (int i = 0; i < 7; i++) fff += ret[5, i] * B[i]; IO.Printer.Out.WriteLine(ggg / (1.0 - fff)); } } public double hoge(int K) { var F = new double[250]; var G = new double[250]; for (int i = K - 1; i >= 0; i--) { for (int j = 1; j <= 6; j++) { if (i + j <= K) { F[i] += 1.0 / 6.0 * F[i + j]; G[i] += 1.0 / 6.0 * G[i + j]; } else { F[i] += 1.0 / 6.0f; } } G[i] += 1.0; } var ans = G[0] / (1.0f - F[0]); return ans; } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region Matrix public class Matrix { int row, col; public double[] mat; public double this[int r, int c] { get { return mat[r * col + c]; } set { mat[r * col + c] = value; } } public Matrix(int r, int c) { if ((r & 1) == 1) r++; if ((c & 1) == 1) c++; row = r; col = c; mat = new double[row * col]; } public static Matrix operator +(Matrix l, Matrix r) { check(l, r); var ret = new Matrix(l.row, l.col); for (int i = 0; i < l.row; i++) for (int j = 0; j < l.col; j++) ret.mat[i * ret.col + j] = l.mat[i * l.col + j] + r.mat[i * r.col + j]; return ret; } public static Matrix operator *(Matrix l, Matrix r) { var ret = new Matrix(l.row, l.col); for (int i = 0; i < l.row; i++) for (int k = 0; k < l.row; k++) for (int j = 0; j < l.col; j++) ret.mat[i * l.col + j] = (ret.mat[i * l.col + j] + l.mat[i * l.col + k] * r.mat[k * l.col + j] ); return ret; } static Matrix[] powmat = new Matrix[64]; public static void otaku(Matrix m) { powmat[0] = m; for (int i = 1; i < 64; i++) powmat[i] = powmat[i - 1] * powmat[i - 1]; } public static Matrix Pow(Matrix m, long n) { var ret = new Matrix(m.row, m.col); for (int i = 0; i < m.row; i++) ret.mat[i * m.col + i] = 1; for (var p = 0; n > 0; n >>= 1, p++) if ((n & 1) == 1) ret = ret * powmat[p]; return ret; } public static Matrix Trans(Matrix m) { var ret = new Matrix(m.col, m.row); for (int i = 0; i < m.row; i++) for (int j = 0; j < m.col; j++) ret.mat[j * m.col + i] = m.mat[i * m.col + j]; return ret; } [System.Diagnostics.Conditional("DEBUG")] static private void check(Matrix a, Matrix b) { if (a.row != b.row || a.col != b.col) throw new Exception("row and col have to be same."); } [System.Diagnostics.Conditional("DEBUG")] static private void checkMul(Matrix a, Matrix b) { if (a.col != b.row) throw new Exception("row and col have to be same."); } } #endregion