#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; const int INF = 1e9; const ll LINF = 1e18; template ostream& operator << (ostream& out,const pair& o){ out << "(" << o.first << "," << o.second << ")"; return out; } template ostream& operator << (ostream& out,const vector V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; } template ostream& operator << (ostream& out,const vector > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; } template ostream& operator << (ostream& out,const map mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; } /* 問題文============================================================ ================================================================= 解説============================================================= ================================================================ */ typedef __int128 lll; istream &operator>>(istream &is,lll &value) { string in; is >> in; value = 0; for (const char &c : in) { if ('0' <= c && c <= '9') value = 10 * value + (c - '0'); } return is; } const int MAX_PRIME = 10000; vector primes; vector is_prime(MAX_PRIME + 1,true); void init_primes(){ is_prime[0] = is_prime[1] = false; for(int i = 2; i <= MAX_PRIME;i++){ if(is_prime[i]){ primes.push_back(i); for(int j = i*2; j <= MAX_PRIME; j+=i) is_prime[j] = false; } } } // return (a * b) % m lll mul_mod(lll a,lll b,lll m){ lll res = 0; lll exp = a % m; while(b){ if(b&1){ res += exp; if(res > m) res -= m; } exp <<= 1; if(exp > m) exp -= m; b >>= 1; } return res; } // return (x ^ k) % m lll pow_mod(lll a, lll b, lll m){ lll res = 1; lll exp = a % m; while(b){ if(b& 1) res = mul_mod(res, exp, m); exp = mul_mod(exp, exp, m); b >>= 1; } return res; } // ミラーラビン素数判定法 // return 判定値 n が 最大times回、乱択的にチェックした時に素数判定されるかどうか bool miller_rabin(lll n, int times) { if (n < 2) return false; if (n == 2) return true; if (!(n & 1)) return false; lll q = n-1; int k = 0; while (q % 2 == 0) { k++; q >>= 1; } // n - 1 = 2^k * q (qは奇素数) // nが素数であれば、下記のいずれかを満たす // (i) a^q ≡ 1 (mod n) // (ii) a^q, a^2q,..., a^(k-1)q のどれかがnを法として-1 // // なので、逆に(i)(ii)いずれも満たしていない時は合成数と判定できる // for (int i = 0; i < times; i++) { lll a = rand() % (n-1) + 1; // 1,..,n-1からランダムに値を選ぶ lll x = pow_mod(a, q, n); // (i)をチェック if (x == 1) continue; // (ii)をチェック bool found = false; for (int j = 0; j < k; j++) { if (x == n-1) { found = true; break; } x = mul_mod(x, x, n); } if (found) continue; return false; } return true; } ll solve(){ init_primes(); ll res = 0; lll N; cin >> N; if(N <= 1000){ for(int W=3;;W++){ vector flag(N+1,0); flag[1] = 1; queue q; q.push(1); int d[4] = {-W,W,-1,1}; while(q.size()){ int now = q.front(); q.pop(); for(int k = 0; k < 4;k++){ if(k==3 && now%W==0)continue; if(k==2 && now%W==1)continue; int next = now + d[k]; if((1<=next && next <= N) && !flag[next] && !is_prime[next]){ flag[next] = 1; q.push(next); } } } if(flag[N]){ res = W; return res; } } }else{ if(N%8==1){ if(miller_rabin(N-8, 1000)) res = 14; else res = 8; }else{ return res = 8; } } return res; } int main(void) { cin.tie(0); ios_base::sync_with_stdio(false); cout << solve() << endl; return 0; }