using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; namespace Program { public class Solver { bool[] primes = MathEx.Sieve(20000); public void Solve() { //Write(17, 8); var s = sc.Scan(); if (s.Length <= 3) { var v = int.Parse(s); for (int i = 3; i < v; i++) { var k = (v + i - 1) / i; var bucket = Enumerate(k, x => new char[i]); var set = new DisjointSet(v); for (int j = 0; j < v; j++) { bucket[j / i][j % i] = (primes[j + 1]) ? 'x' : 'o'; if (primes[j + 1]) continue; var u = (j / i - 1); if (u >= 0 && !primes[j + 1 - i]) set.Unite(j, j - i); if (j % i > 0 && !primes[j]) set.Unite(j, j - 1); } //foreach (var x in bucket) IO.Printer.Out.WriteLine(x.AsString()); if (set.IsUnited(0, v - 1)) { IO.Printer.Out.WriteLine(i); return; } } } else { var v = BigInteger.Parse(s) - 8; if (v % 8 != 1) { IO.Printer.Out.WriteLine(8); } else { long u; if (long.TryParse(s, out u) && isPrime(u - 8)) { IO.Printer.Out.WriteLine(14); } else IO.Printer.Out.WriteLine(8); } } } static public long ModPow(long x, long n, long mod) { long r = 1; while (n > 0) { if ((n & 1) == 1) r = r * x % mod; x = (x * x) % mod; n >>= 1; } return r; } bool suspect(long a, long s, long d, long n) { var x = ModPow(a, d, n); if (x == 1) return true; for (int r = 0; r < s; ++r) { if (x == n - 1) return true; x = x * x % n; } return false; } // {2,7,61,-1} is for n < 4759123141 (= 2^32) // {2,3,5,7,11,13,17,19,23,-1} is for n < 10^16 (at least) bool isPrime(long n) { if (n >= 5000000000000000) return true; for (long u = 2; u * u <= n; u++) { if (n % u == 0) return false; } return true; /* if (n <= 1 || (n > 2 && n % 2 == 0)) return false; var test = new int[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, -1 }; long d = n - 1, s = 0; while (d % 2 == 0) { ++s; d /= 2; } for (int i = 0; test[i] < n && test[i] != -1; ++i) if (!suspect(test[i], s, d, n)) return false; return true; */ } public void Write(int v, int i) { var k = (v + i - 1) / i; var bucket = Enumerate(k, x => new char[i]); var set = new DisjointSet(v); for (int j = 0; j < v; j++) { bucket[j / i][j % i] = (primes[j + 1]) ? 'x' : 'o'; if (primes[j + 1]) continue; var u = (j / i - 1); if (u >= 0 && !primes[j + 1 - i]) set.Unite(j, j - i); if (j % i > 0 && !primes[j]) set.Unite(j, j - 1); } IO.Printer.Out.WriteLine("{0} {1}", v, i); foreach (var x in bucket) IO.Printer.Out.WriteLine(x.AsString()); } 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 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, IEnumerable source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, IEnumerable 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 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); } } } 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 sieve static public partial class MathEx { static public bool[] Sieve(int p) { var isPrime = new bool[p + 1]; for (int i = 2; i <= p; i++) isPrime[i] = true; for (int i = 2; i * i <= p; i++) if (!isPrime[i]) continue; else for (int j = i * i; j <= p; j += i) isPrime[j] = false; return isPrime; } } #endregion #region DisjointSet public class DisjointSet { public int[] par, ranks, count; public DisjointSet(int n) { par = new int[n]; count = new int[n]; for (int i = 0; i < n; i++) { par[i] = i; count[i] = 1; } ranks = new int[n]; } public int this[int id] { get { return (par[id] == id) ? id : this[par[id]]; } } public bool Unite(int x, int y) { x = this[x]; y = this[y]; if (x == y) return false; if (ranks[x] < ranks[y]) { par[x] = y; count[y] += count[x]; } else { par[y] = x; count[x] += count[y]; if (ranks[x] == ranks[y]) ranks[x]++; } return true; } public int Size(int x) { return count[this[x]]; } public bool IsUnited(int x, int y) { return this[x] == this[y]; } } #endregion