using System; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Globalization; using System.IO; using System.Text; using System.Linq; using E = System.Linq.Enumerable; internal partial class Solver { public void Run() { var n = nl(); var mod = ModInt.SetModValue(1000000000 + 7); var p = new ModInt(1) / 6; var M = new ModMatrix(new ModInt[6, 6] { { 0, 1, 0, 0, 0, 0 }, { 0, 0, 1, 0, 0, 0 }, { 0, 0, 0, 1, 0, 0 }, { 0, 0, 0, 0, 1, 0 }, { 0, 0, 0, 0, 0, 1 }, { p, p, p, p, p, p }, }); //var v = var b = new ModInt[6]; b[0] = 1; for (int i = 1; i < b.Length; i++) { for (int j = 0; j < i; j++) { b[i] += b[j] / 6; } } var x = ModMatrix.Pow(M, n) * ModMatrix.TransposeFrom(b); cout.WriteLine(x[0,0]); } } public class ModMatrix { public int Row { get; private set; } public int Col { get; private set; } private ModInt[] Data; public ModMatrix(int row, int col) { Row = row; Col = col; Data = new ModInt[Row * Col]; } public ModMatrix(ModInt[,] array) : this(array.GetLength(0), array.GetLength(1)) { int index = 0; for (int i = 0; i < Row; i++) { for (int j = 0; j < Col; j++) { Data[index++] = array[i, j]; } } } public static ModMatrix TransposeFrom(IList list) { var count = list.Count; var result = new ModInt[count, 1]; for (int i = 0; i < count; i++) { result[i, 0] = list[i]; } return new ModMatrix(result); } public ModInt this[int row, int col] { set { Data[row * Col + col] = value; } get { return Data[row * Col + col]; } } public static ModMatrix UnitMatrix(int n) { var matrix = new ModMatrix(n, n); for (int i = 0; i < n; i++) { matrix[i, i] = 1; } return matrix; } public static ModMatrix operator +(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, A.Col); for (int i = 0; i < C.Data.Length; i++) { C.Data[i] = A.Data[i] + B.Data[i]; } return C; } public static ModMatrix operator -(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, A.Col); for (int i = 0; i < C.Data.Length; i++) { C.Data[i] = A.Data[i] - B.Data[i]; } return C; } public static ModMatrix operator *(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, B.Col); for (int i = 0; i < A.Row; i++) { for (int j = 0; j < B.Col; j++) { var val = C[i, j]; for (int k = 0; k < A.Col; k++) { val += A[i, k] * B[k, j]; } C[i, j] = val; } } return C; } public static ModMatrix Pow(ModMatrix A, long n) { if (n == 0) { return UnitMatrix(A.Row); } if (n == 1) { return A; } ModMatrix result = A.Clone(), t = A.Clone(); n--; while (n > 0) { if ((n & 1) != 0) { result = result * t; } t = t * t; n >>= 1; } return result; } public ModMatrix Clone() { return new ModMatrix(Row, Col) { Data = Data.Clone() as ModInt[] }; } private static void Swap(ref T a, ref T b) { var t = a; a = b; b = t; } public static ModInt Determinant(ModMatrix matrix) { if (matrix.Row != matrix.Col) { throw new ArgumentException(); } int n = matrix.Col; var m = new ModInt[n][]; for (int i = 0; i < n; i++) { var r = new ModInt[n]; for (int j = 0; j < n; j++) { r[j] = matrix[i, j]; } m[i] = r; } ModInt d = 1; for (int i = 0; i < n; i++) { int targetRow = -1; ModInt pivot = 0; for (int r = i; r < n; r++) { var row = m[r]; if (row[i] != 0) { targetRow = r; pivot = row[i]; break; } } if (targetRow == -1) { return 0; } if (i != targetRow) { Swap(ref m[i], ref m[targetRow]); d = -d; } d *= pivot; var mi = m[i]; var invPivot = 1 / pivot; for (int r = i + 1; r < n; r++) { var row = m[r]; var weight = row[i] * invPivot; if (weight == 0) { continue; } for (int k = i + 1; k < n; k++) { row[k] -= weight * mi[k]; } } } return d; } } public struct ModInt : IEquatable { private static int mod = 0; private long _value; public ModInt(long x) { _value = x; Normalize(); } private static long RegularMod(long x, int mod) { if (x >= mod) { if (x < 2 * mod) { return x - mod; } return x % mod; } if (x >= 0) { return x; } x = mod - RegularMod(-x, mod); if (x == mod) { return 0; } return x; } public static int SetModValue(int m) { return mod = m; } private void Normalize() { _value = RegularMod(_value, mod); } public override string ToString() { return _value.ToString(CultureInfo.InvariantCulture); } public int ToInt() { return (int)_value; } public static bool operator ==(ModInt c1, ModInt c2) { return c1._value == c2._value; } public static bool operator !=(ModInt c1, ModInt c2) { return !(c1 == c2); } public static ModInt operator +(ModInt x, ModInt y) { return new ModInt(x._value + y._value); } public static ModInt operator -(ModInt x, ModInt y) { return new ModInt(x._value - y._value); } public static ModInt operator -(ModInt x) { return new ModInt(-x._value); } public static ModInt operator *(ModInt x, ModInt y) { return new ModInt(x._value * y._value); } public static ModInt operator /(ModInt x, ModInt y) { return new ModInt(x._value * Inverse(y._value, mod)); } public static ModInt operator ++(ModInt x) { return x + 1; } public static ModInt operator --(ModInt x) { return x - 1; } public static ModInt Pow(ModInt x, long n) { ModInt r = 1; while (n > 0) { if ((n & 1) != 0) { r *= x; } x *= x; n >>= 1; } return r; } private static long ExtendedGcd(long a, long b, ref long x, ref long y) { if (b == 0) { x = 1; y = 0; return a; } else { var d = ExtendedGcd(b, a % b, ref y, ref x); y -= a / b * x; return d; } } private static long Inverse(long a, long mod) { long x = 0, y = 0; if (ExtendedGcd(a, mod, ref x, ref y) == 1) { return (x + mod) % mod; } else { throw new Exception("Invalid inverse " + a + " " + mod); } } public static implicit operator ModInt(long x) { return new ModInt(x); } public override bool Equals(object obj) { if (obj == null) { return false; } return _value.Equals(((ModInt)obj)._value); } public override int GetHashCode() { return _value.GetHashCode(); } public bool Equals(ModInt other) { return _value.Equals(other._value); } } // PREWRITEN CODE BEGINS FROM HERE static public class StringExtensions { static public string JoinToString(this IEnumerable source, string separator = " ") { return string.Join(separator, source); } } internal partial class Solver : Scanner { public static void Main() { #if LOCAL byte[] inputBuffer = new byte[1000000]; var inputStream = Console.OpenStandardInput(inputBuffer.Length); using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) { Console.SetIn(reader); new Solver(Console.In, Console.Out).Run(); } #else Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver(Console.In, Console.Out).Run(); Console.Out.Flush(); #endif } #pragma warning disable IDE0052 private readonly TextReader cin; private readonly TextWriter cout; private readonly TextWriter cerr; #pragma warning restore IDE0052 public Solver(TextReader reader, TextWriter writer) : base(reader) { cin = reader; cout = writer; cerr = Console.Error; } public Solver(string input, TextWriter writer) : this(new StringReader(input), writer) { } #pragma warning disable IDE1006 #pragma warning disable IDE0051 private int ni() { return NextInt(); } private int[] ni(int n) { return NextIntArray(n); } private long nl() { return NextLong(); } private long[] nl(int n) { return NextLongArray(n); } private double nd() { return NextDouble(); } private double[] nd(int n) { return NextDoubleArray(n); } private string ns() { return Next(); } private string[] ns(int n) { return NextArray(n); } #pragma warning restore IDE1006 #pragma warning restore IDE0051 } internal static class LinqPadExtension { [Conditional("DEBUG")] public static void Dump(this T obj) { #if DEBUG LINQPad.Extensions.Dump(obj); #endif } } public class Scanner { private readonly TextReader Reader; private readonly CultureInfo ci = CultureInfo.InvariantCulture; private readonly char[] buffer = new char[2 * 1024]; private int cursor = 0, length = 0; private string Token; private readonly StringBuilder sb = new StringBuilder(1024); public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { Reader = reader; } public int NextInt() { return checked((int)NextLong()); } public long NextLong() { var s = Next(); long r = 0; int i = 0; bool negative = false; if (s[i] == '-') { negative = true; i++; } for (; i < s.Length; i++) { r = r * 10 + (s[i] - '0'); #if DEBUG if (!char.IsDigit(s[i])) throw new FormatException(); #endif } return negative ? -r : r; } public double NextDouble() { return double.Parse(Next(), ci); } public string[] NextArray(int size) { string[] array = new string[size]; for (int i = 0; i < size; i++) { array[i] = Next(); } return array; } public int[] NextIntArray(int size) { int[] array = new int[size]; for (int i = 0; i < size; i++) { array[i] = NextInt(); } return array; } public long[] NextLongArray(int size) { long[] array = new long[size]; for (int i = 0; i < size; i++) { array[i] = NextLong(); } return array; } public double[] NextDoubleArray(int size) { double[] array = new double[size]; for (int i = 0; i < size; i++) { array[i] = NextDouble(); } return array; } public string Next() { if (Token == null) { if (!StockToken()) { throw new Exception(); } } var token = Token; Token = null; return token; } public bool HasNext() { if (Token != null) { return true; } return StockToken(); } private bool StockToken() { while (true) { sb.Clear(); while (true) { if (cursor >= length) { cursor = 0; if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) { break; } } var c = buffer[cursor++]; if (33 <= c && c <= 126) { sb.Append(c); } else { if (sb.Length > 0) break; } } if (sb.Length > 0) { Token = sb.ToString(); return true; } return false; } } }