#nullable enable using System.Numerics; void Run() { var n = Int(); ModInt.Mod = n; var ans = ((ModInt)1).DiscreteLog((ModInt)10, int.MaxValue / 2); Out(ans); } #region AtCoderIO _io_; var _backend_ = new StandardIOBackend(); _io_ = new(){ Backend = _backend_ }; Run(); _backend_.Flush(); string String() => _io_.Next(); int Int() => int.Parse(String()); void Out(object? x, string? sep = null) => _io_.Out(x, sep); class AtCoderIO { public required StandardIOBackend Backend { get; init; } Memory<string> _input = Array.Empty<string>(); int _iter = 0; public string Next() { while (_iter >= _input.Length) (_input, _iter) = (Backend.ReadLine().Trim().Split(' '), 0); return _input.Span[_iter++]; } public void Out(object? x, string? separator = null) { if (x == null) return; separator ??= Environment.NewLine; if (x is System.Collections.IEnumerable a and not string) { var objects = a.Cast<object>(); if (separator == Environment.NewLine && !objects.Any()) return; x = string.Join(separator, objects); } Backend.WriteLine(x); } } class StandardIOBackend { readonly StreamReader _sr = new(Console.OpenStandardInput()); readonly StreamWriter _sw = new(Console.OpenStandardOutput()) { AutoFlush = false }; public string ReadLine() => _sr.ReadLine()!; public void WriteLine(object? value) => _sw.WriteLine(value); public void Flush() => _sw.Flush(); } #endregion interface IAdditiveGroup<T> : IAdditiveIdentity<T, T>, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T> where T : IAdditiveGroup<T> { T AdditiveInverse(); } interface IMultiplicativeGroup<T> : IMultiplicativeIdentity<T, T>, IMultiplyOperators<T, T, T>, IDivisionOperators<T, T, T> where T : IMultiplicativeGroup<T> { T MultiplicativeInverse(); } readonly record struct ModInt : IEqualityOperators<ModInt, ModInt, bool>, IAdditiveGroup<ModInt>, IMultiplicativeGroup<ModInt> { public static int Mod = 0; int V { get; init; } public ModInt(long value) { var v = value % Mod; if (v < 0) v += Mod; V = (int)v; } static ModInt New(int value) => new(){ V = value }; public static implicit operator ModInt(long v) => new(v); public static implicit operator int(ModInt modInt) => modInt.V; public static ModInt AdditiveIdentity => New(0); public static ModInt operator +(ModInt a, ModInt b) { var v = a.V + b.V; if (v >= Mod) v -= Mod; return New(v); } public ModInt AdditiveInverse() { if (V == 0) return AdditiveIdentity; return New(Mod - V); } public static ModInt operator -(ModInt a, ModInt b) { var v = a.V - b.V; if (v < 0) v += Mod; return New(v); } public static ModInt MultiplicativeIdentity => New(1); public static ModInt operator *(ModInt a, ModInt b) => New((int)((long)a.V * b.V % Mod)); public ModInt MultiplicativeInverse() { if (V == 0) throw new DivideByZeroException(); var (d, x, _) = ExtendedGCD(V, Mod); if (d > 1) throw new DivideByZeroException(); return x; } public static ModInt operator /(ModInt a, ModInt b) => a * b.MultiplicativeInverse(); static long Power(long v, ulong p, long mod) { var (res, k) = (1L, v); while (p > 0) { if ((p & 1) > 0) res = res * k % mod; k = k * k % mod; p >>= 1; } return res; } public ModInt Power(long p) => p < 0 ? (MultiplicativeIdentity / V).Power(-p) : Power(V, (ulong)p, Mod); static (long d, long x, long y) ExtendedGCD(long a, long b) { var (x0, y0, x1, y1) = (1L, 0L, 0L, 1L); while (b != 0) { var q = a / b; (a, b) = (b, a - q * b); (x0, y0, x1, y1) = (x1, y1, x0 - q * x1, y0 - q * y1); } return (a, x0, y0); } public override string ToString() => V.ToString(); } static class Extensions { public static T[] Repeat<T>(this int time, Func<T> F) => Enumerable.Range(0, time).Select(_ => F()).ToArray(); public static long? DiscreteLog<T>(this T a, T b, long max) where T : IMultiplyOperators<T, T, T>, IMultiplicativeIdentity<T, T> { var q = 1; while (q * q < max) q++; var smallSteps = new HashSet<T>(); { var v = a; for (var i = 1; i <= q; i++) { v *= b; smallSteps.Add(v); } } var giantStep = b; for (var i = 2; i <= q; i++) giantStep *= b; var l = T.MultiplicativeIdentity; var yellow = false; for (var i = 0; i < q; i++) { var g = l * giantStep; if (smallSteps.Contains(g)) { var v = l; for (var j = 1; j <= q; j++) { v *= b; if (v.Equals(a)) { var res = (long)i * q + j; if (res > max) return null; return res; } } if (yellow) return null; yellow = true; } l = g; } return null; } }