using System; using System.Collections.Generic; using System.Globalization; using System.IO; using System.Linq; using System.Numerics; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Text; namespace YukiCoder { class Program { static void Main() { using var cin = new Scanner(); long n = cin.Long(); long ans = n - 1; long m = n; int ii = 1; for (int i = 9; i > 0; i--) { if (n % i == 0) { m = n / i; ii = i; break; } } if (m == 1) { Console.WriteLine(2); return; } for (long j = 2; j * j <= n; j++) { BigInteger r = j; BigInteger sum = 1 + r; while (true) { if (sum >= m) { if (sum == m && j >= ii) { ans.UpdateMin(j); } break; } r *= j; sum += r; } } Console.WriteLine(ans); } } public struct BitFlag { public static BitFlag Begin() => 0; public static BitFlag End(int bitCount) => 1 << bitCount; public static BitFlag FromBit(int bitNumber) => 1 << bitNumber; private readonly int flags_; public int Flag => flags_; public bool this[int bitNumber] => (flags_ & (1 << bitNumber)) != 0; public BitFlag(int flags) { flags_ = flags; } public bool Has(BitFlag target) => (flags_ & target.flags_) == target.flags_; public bool Has(int target) => (flags_ & target) == target; public bool HasBit(int bitNumber) => (flags_ & (1 << bitNumber)) != 0; public BitFlag OrBit(int bitNumber) => (flags_ | (1 << bitNumber)); public BitFlag AndBit(int bitNumber) => (flags_ & (1 << bitNumber)); public BitFlag XorBit(int bitNumber) => (flags_ ^ (1 << bitNumber)); public static BitFlag operator ++(BitFlag src) => new BitFlag(src.flags_ + 1); public static BitFlag operator --(BitFlag src) => new BitFlag(src.flags_ - 1); public static BitFlag operator |(BitFlag lhs, BitFlag rhs) => new BitFlag(lhs.flags_ | rhs.flags_); public static BitFlag operator |(BitFlag lhs, int rhs) => new BitFlag(lhs.flags_ | rhs); public static BitFlag operator |(int lhs, BitFlag rhs) => new BitFlag(lhs | rhs.flags_); public static BitFlag operator &(BitFlag lhs, BitFlag rhs) => new BitFlag(lhs.flags_ & rhs.flags_); public static BitFlag operator &(BitFlag lhs, int rhs) => new BitFlag(lhs.flags_ & rhs); public static BitFlag operator &(int lhs, BitFlag rhs) => new BitFlag(lhs & rhs.flags_); public static bool operator <(BitFlag lhs, BitFlag rhs) => lhs.flags_ < rhs.flags_; public static bool operator <(BitFlag lhs, int rhs) => lhs.flags_ < rhs; public static bool operator <(int lhs, BitFlag rhs) => lhs < rhs.flags_; public static bool operator >(BitFlag lhs, BitFlag rhs) => lhs.flags_ > rhs.flags_; public static bool operator >(BitFlag lhs, int rhs) => lhs.flags_ > rhs; public static bool operator >(int lhs, BitFlag rhs) => lhs > rhs.flags_; public static bool operator <=(BitFlag lhs, BitFlag rhs) => lhs.flags_ <= rhs.flags_; public static bool operator <=(BitFlag lhs, int rhs) => lhs.flags_ <= rhs; public static bool operator <=(int lhs, BitFlag rhs) => lhs <= rhs.flags_; public static bool operator >=(BitFlag lhs, BitFlag rhs) => lhs.flags_ >= rhs.flags_; public static bool operator >=(BitFlag lhs, int rhs) => lhs.flags_ >= rhs; public static bool operator >=(int lhs, BitFlag rhs) => lhs >= rhs.flags_; public static implicit operator BitFlag(int t) => new BitFlag(t); public static implicit operator int(BitFlag t) => t.flags_; public override string ToString() => $"{Convert.ToString(flags_, 2).PadLeft(32, '0')} ({flags_})"; [MethodImpl(MethodImplOptions.AggressiveInlining)] public void ForEachSubBits(Action action) { for (BitFlag sub = flags_; sub >= 0; --sub) { sub &= flags_; action(sub); } } } public class HashMap : Dictionary { private readonly Func initialzier_; public HashMap(Func initialzier) : base() { initialzier_ = initialzier; } public HashMap(Func initialzier, int capacity) : base(capacity) { initialzier_ = initialzier; } new public TValue this[TKey key] { get { if (TryGetValue(key, out TValue value)) { return value; } else { var init = initialzier_(key); base[key] = init; return init; } } set { base[key] = value; } } public HashMap Merge( HashMap src, Func mergeValues) { foreach (var key in src.Keys) { this[key] = mergeValues(this[key], src[key]); } return this; } } public struct ModInt { //public const long P = 1000000007; public const long P = 998244353; public const long ROOT = 3; // (924844033, 5) // (998244353, 3) // (1012924417, 5) // (167772161, 3) // (469762049, 3) // (1224736769, 3) private long value_; public ModInt(long value) => value_ = value; public ModInt(long value, bool mods) { if (mods) { value %= P; if (value < 0) { value += P; } } value_ = value; } public static ModInt operator +(ModInt lhs, ModInt rhs) { lhs.value_ = (lhs.value_ + rhs.value_) % P; return lhs; } public static ModInt operator +(long lhs, ModInt rhs) { rhs.value_ = (lhs + rhs.value_) % P; return rhs; } public static ModInt operator +(ModInt lhs, long rhs) { lhs.value_ = (lhs.value_ + rhs) % P; return lhs; } public static ModInt operator -(ModInt lhs, ModInt rhs) { lhs.value_ = (P + lhs.value_ - rhs.value_) % P; return lhs; } public static ModInt operator -(long lhs, ModInt rhs) { rhs.value_ = (P + lhs - rhs.value_) % P; return rhs; } public static ModInt operator -(ModInt lhs, long rhs) { lhs.value_ = (P + lhs.value_ - rhs) % P; return lhs; } public static ModInt operator *(ModInt lhs, ModInt rhs) { lhs.value_ = lhs.value_ * rhs.value_ % P; return lhs; } public static ModInt operator *(long lhs, ModInt rhs) { rhs.value_ = lhs * rhs.value_ % P; return rhs; } public static ModInt operator *(ModInt lhs, long rhs) { lhs.value_ = lhs.value_ * rhs % P; return lhs; } public static ModInt operator /(ModInt lhs, ModInt rhs) { long exp = P - 2; while (exp > 0) { if (exp % 2 > 0) { lhs *= rhs; } rhs *= rhs; exp /= 2; } return lhs; } public static implicit operator ModInt(long n) => new ModInt(n, true); public static ModInt Inverse(ModInt value) => Pow(value, P - 2); public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k); public static ModInt Pow(long value, long k) { long ret = 1; for (k %= P - 1; k > 0; k >>= 1, value = value * value % P) { if ((k & 1) == 1) { ret = ret * value % P; } } return new ModInt(ret); } public static Span NumberTheoreticTransform( Span values, bool inverses = false) { var mods = new ModInt[values.Length]; for (int i = 0; i < mods.Length; i++) { mods[i] = new ModInt(values[i]); } return NumberTheoreticTransform(mods, inverses); } public static Span NumberTheoreticTransform( Span values, bool inverses = false) { var mods = new ModInt[values.Length]; for (int i = 0; i < mods.Length; i++) { mods[i] = new ModInt(values[i]); } return NumberTheoreticTransform(mods, inverses); } public static Span NumberTheoreticTransform( Span a, bool inverses = false) { int n = a.Length; if (n == 1) { return a; } var b = new ModInt[n].AsSpan(); int r = inverses ? (int)(P - 1 - (P - 1) / n) : (int)((P - 1) / n); ModInt s = Pow(ROOT, r); var kp = new ModInt[n / 2 + 1]; kp.AsSpan().Fill(1); for (int i = 0; i < n / 2; ++i) { kp[i + 1] = kp[i] * s; } int l = n / 2; for (int i = 1; i < n; i <<= 1, l >>= 1) { r = 0; for (int j = 0; j < l; ++j, r += i) { s = kp[i * j]; for (int k = 0; k < i; ++k) { var p = a[k + r]; var q = a[k + r + n / 2]; b[k + 2 * r] = p + q; b[k + 2 * r + i] = (p - q) * s; } } var temp = a; a = b; b = temp; } if (inverses) { s = Inverse(n); for (int i = 0; i < n; i++) { a[i] = a[i] * s; } } return a; } public static ModInt[,] NumberTheoreticTransform2D(ModInt[,] a, bool inverses = false) { int h = a.GetLength(0); int w = a.GetLength(1); if (h == 1 && w == 1) { return a; } var b = new ModInt[h, w]; { int n = w; int r = inverses ? (int)(P - 1 - (P - 1) / n) : (int)((P - 1) / n); ModInt s = Pow(ROOT, r); var kp = new ModInt[n / 2 + 1]; kp.AsSpan().Fill(1); for (int i = 0; i < n / 2; ++i) { kp[i + 1] = kp[i] * s; } for (int y = 0; y < h; y++) { int l = n / 2; for (int i = 1; i < n; i <<= 1, l >>= 1) { r = 0; for (int j = 0; j < l; ++j, r += i) { s = kp[i * j]; for (int k = 0; k < i; ++k) { var p = a[y, k + r]; var q = a[y, k + r + n / 2]; b[y, k + 2 * r] = p + q; b[y, k + 2 * r + i] = (p - q) * s; } } var temp = a; a = b; b = temp; } if (inverses) { s = Inverse(n); for (int i = 0; i < n; i++) { a[y, i] = a[y, i] * s; } } } } for (int i = 0; i < h; i++) { for (int j = 0; j < w; j++) { b[h, w] = 0; } } { int n = h; int r = inverses ? (int)(P - 1 - (P - 1) / n) : (int)((P - 1) / n); ModInt s = Pow(ROOT, r); var kp = new ModInt[n / 2 + 1]; kp.AsSpan().Fill(1); for (int i = 0; i < n / 2; ++i) { kp[i + 1] = kp[i] * s; } for (int x = 0; x < w; x++) { int l = n / 2; for (int i = 1; i < n; i <<= 1, l >>= 1) { r = 0; for (int j = 0; j < l; ++j, r += i) { s = kp[i * j]; for (int k = 0; k < i; ++k) { var p = a[k + r, x]; var q = a[k + r + n / 2, x]; b[k + 2 * r, x] = p + q; b[k + 2 * r + i, x] = (p - q) * s; } } var temp = a; a = b; b = temp; } if (inverses) { s = Inverse(n); for (int i = 0; i < n; i++) { a[i, x] = a[i, x] * s; } } } } return a; } public static Span Convolve(ReadOnlySpan a, ReadOnlySpan b) { int resultLength = a.Length + b.Length - 1; int nttLenght = 1; while (nttLenght < resultLength) { nttLenght <<= 1; } var aa = new ModInt[nttLenght]; a.CopyTo(aa); var bb = new ModInt[nttLenght]; b.CopyTo(bb); var fa = NumberTheoreticTransform(aa); var fb = NumberTheoreticTransform(bb); for (int i = 0; i < nttLenght; i++) { fa[i] *= fb[i]; } var convolved = NumberTheoreticTransform(fa, true); return convolved.Slice(0, resultLength); } public long ToLong() => value_; public override string ToString() => value_.ToString(); } public static class Helper { [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void UpdateMin(this ref T target, T value) where T : struct, IComparable => target = target.CompareTo(value) > 0 ? value : target; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void UpdateMin(this ref T target, T value, Action onUpdated) where T : struct, IComparable { if (target.CompareTo(value) > 0) { target = value; onUpdated(value); } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void UpdateMax(this ref T target, T value) where T : struct, IComparable => target = target.CompareTo(value) < 0 ? value : target; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void UpdateMax(this ref T target, T value, Action onUpdated) where T : struct, IComparable { if (target.CompareTo(value) < 0) { target = value; onUpdated(value); } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[] Array1(int n, T initialValue) where T : struct => new T[n].Fill(initialValue); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[] Array1(int n, Func initializer) => Enumerable.Range(0, n).Select(x => initializer(x)).ToArray(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[] Fill(this T[] array, T value) where T : struct { array.AsSpan().Fill(value); return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,] Array2(int n, int m, T initialValule) where T : struct => new T[n, m].Fill(initialValule); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,] Array2(int n, int m, Func initializer) { var array = new T[n, m]; for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { array[i, j] = initializer(i, j); } } return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,] Fill(this T[,] array, T initialValue) where T : struct { MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(initialValue); return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span AsSpan(this T[,] array, int i) => MemoryMarshal.CreateSpan(ref array[i, 0], array.GetLength(1)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,,] Array3(int n1, int n2, int n3, T initialValue) where T : struct => new T[n1, n2, n3].Fill(initialValue); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,,] Fill(this T[,,] array, T initialValue) where T : struct { MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(initialValue); return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span AsSpan(this T[,,] array, int i, int j) => MemoryMarshal.CreateSpan(ref array[i, j, 0], array.GetLength(2)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,,,] Array4(int n1, int n2, int n3, int n4, T initialValue) where T : struct => new T[n1, n2, n3, n4].Fill(initialValue); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[,,,] Fill(this T[,,,] array, T initialValue) where T : struct { MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(initialValue); return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Span AsSpan(this T[,,,] array, int i, int j, int k) => MemoryMarshal.CreateSpan(ref array[i, j, k, 0], array.GetLength(3)); private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 }; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void DoIn4(int i, int j, int imax, int jmax, Action action) { for (int dn = 0; dn < 4; ++dn) { int d4i = i + delta4_[dn]; int d4j = j + delta4_[dn + 1]; if ((uint)d4i < (uint)imax && (uint)d4j < (uint)jmax) { action(d4i, d4j); } } } private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 }; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void DoIn8(int i, int j, int imax, int jmax, Action action) { for (int dn = 0; dn < 8; ++dn) { int d8i = i + delta8_[dn]; int d8j = j + delta8_[dn + 1]; if ((uint)d8i < (uint)imax && (uint)d8j < (uint)jmax) { action(d8i, d8j); } } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void ForEachSubBits(int bit, Action action) { for (int sub = bit; sub >= 0; --sub) { sub &= bit; action(sub); } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static string Reverse(string src) { var chars = src.ToCharArray(); for (int i = 0, j = chars.Length - 1; i < j; ++i, --j) { var tmp = chars[i]; chars[i] = chars[j]; chars[j] = tmp; } return new string(chars); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static string Join(this IEnumerable values, string separator = "") => string.Join(separator, values); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static string JoinNL(this IEnumerable values) => string.Join(Environment.NewLine, values); } public static class Extensions { public static uint PopCount(uint bits) { bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555); bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333); bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f); bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff); return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int PopCount(this BitFlag bit) => (int)PopCount((uint)bit.Flag); } public class Scanner : IDisposable { private const int BUFFER_SIZE = 1024; private const int ASCII_CHAR_BEGIN = 33; private const int ASCII_CHAR_END = 126; private readonly string filePath_; private readonly Stream stream_; private readonly byte[] buf_ = new byte[BUFFER_SIZE]; private int length_ = 0; private int index_ = 0; private bool isEof_ = false; public Scanner(string file = "") { if (string.IsNullOrWhiteSpace(file)) { stream_ = Console.OpenStandardInput(); } else { filePath_ = file; stream_ = new FileStream(file, FileMode.Open); } Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); } public void Dispose() { Console.Out.Flush(); stream_.Dispose(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public char Char() { byte b; do { b = Read(); } while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b); return (char)b; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public string Next() { var sb = new StringBuilder(); for (var b = Char(); b >= ASCII_CHAR_BEGIN && b <= ASCII_CHAR_END; b = (char)Read()) { sb.Append(b); } return sb.ToString(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public string[] ArrayString(int length) { var array = new string[length]; for (int i = 0; i < length; ++i) { array[i] = Next(); } return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int Int() => (int)Long(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public int Int(int offset) => Int() + offset; [MethodImpl(MethodImplOptions.AggressiveInlining)] public (int, int) Int2(int offset = 0) => (Int(offset), Int(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (int, int, int) Int3(int offset = 0) => (Int(offset), Int(offset), Int(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (int, int, int, int) Int4(int offset = 0) => (Int(offset), Int(offset), Int(offset), Int(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public int[] ArrayInt(int length, int offset = 0) { var array = new int[length]; for (int i = 0; i < length; ++i) { array[i] = Int(offset); } return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public long Long() { long ret = 0; byte b; bool 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'; } } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public long Long(long offset) => Long() + offset; [MethodImpl(MethodImplOptions.AggressiveInlining)] public (long, long) Long2(long offset = 0) => (Long(offset), Long(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (long, long, long) Long3(long offset = 0) => (Long(offset), Long(offset), Long(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (long, long, long, long) Long4(long offset = 0) => (Long(offset), Long(offset), Long(offset), Long(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public long[] ArrayLong(int length, long offset = 0) { var array = new long[length]; for (int i = 0; i < length; ++i) { array[i] = Long(offset); } return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public BigInteger Big() => new BigInteger(Long()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public BigInteger Big(long offset) => Big() + offset; [MethodImpl(MethodImplOptions.AggressiveInlining)] public (BigInteger, BigInteger) Big2(long offset = 0) => (Big(offset), Big(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (BigInteger, BigInteger, BigInteger) Big3(long offset = 0) => (Big(offset), Big(offset), Big(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (BigInteger, BigInteger, BigInteger, BigInteger) Big4(long offset = 0) => (Big(offset), Big(offset), Big(offset), Big(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public BigInteger[] ArrayBig(int length, long offset = 0) { var array = new BigInteger[length]; for (int i = 0; i < length; ++i) { array[i] = Big(offset); } return array; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public double Double() => double.Parse(Next(), CultureInfo.InvariantCulture); [MethodImpl(MethodImplOptions.AggressiveInlining)] public double Double(double offset) => Double() + offset; [MethodImpl(MethodImplOptions.AggressiveInlining)] public (double, double) Double2(double offset = 0) => (Double(offset), Double(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (double, double, double) Double3(double offset = 0) => (Double(offset), Double(offset), Double(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public (double, double, double, double) Double4(double offset = 0) => (Double(offset), Double(offset), Double(offset), Double(offset)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public double[] ArrayDouble(int length, double offset = 0) { var array = new double[length]; for (int i = 0; i < length; ++i) { array[i] = Double(offset); } return array; } private byte Read() { if (isEof_) { throw new EndOfStreamException(); } if (index_ >= length_) { index_ = 0; if ((length_ = stream_.Read(buf_, 0, BUFFER_SIZE)) <= 0) { isEof_ = true; return 0; } } return buf_[index_++]; } public void Save(string text) { if (string.IsNullOrWhiteSpace(filePath_)) { return; } File.WriteAllText(filePath_ + "_output.txt", text); } } }