#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); ll mod_pow(ll x, ll n, ll m) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 2; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } struct bigint { string s; bigint() {}; bigint(ll n) { s = to_string(n); }; bigint(string t) { s = t; }; }; bool operator==(const bigint& a, const bigint& b) { return a.s == b.s; }; bool operator==(const bigint& a, const int& b) { return a.s == to_string(b); }; bool operator!=(const bigint& a, const bigint& b) { return !(a == b); }; bool operator!=(const bigint& a, const int& b) { return a != to_string(b); }; bool operator<(const bigint& a, const bigint& b) { if (a.s.length() != b.s.length())return a.s.length() < b.s.length(); return a.s < b.s; } bool operator>(const bigint& a, const bigint& b) { if (a.s.length() != b.s.length())return a.s.length() > b.s.length(); return a.s > b.s; } bool operator>=(const bigint& a, const bigint& b) { return !(a < b); } bool operator<=(const bigint& a, const bigint& b) { return !(a > b); } bigint operator+(const bigint& a, const bigint& b) { int len = max(a.s.length(), b.s.length()); bigint ret; bool f = false; rep(i, len) { int c = 0; if (f)c = 1, f = false; int j = a.s.length() - 1 - i; if (j >= 0)c += a.s[j] - '0'; j = b.s.length() - 1 - i; if (j >= 0)c += b.s[j] - '0'; if (c >= 10)f = true, c -= 10; ret.s.push_back('0' + c); } if (f)ret.s.push_back('1'); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator+(const bigint& a, const int b) { return a + bigint(b); } bigint operator-(const bigint& a, const bigint& b) { int len = max(a.s.length(), b.s.length()); bigint ret; bool f = false; rep(i, len) { int c = 0; if (f)c = -1, f = false; int j = a.s.length() - 1 - i; if (j >= 0)c += a.s[j] - '0'; j = b.s.length() - 1 - i; if (j >= 0)c -= b.s[j] - '0'; if (c < 0)f = true, c += 10; ret.s.push_back('0' + c); } while (ret.s.size() > 1 && ret.s.back() == '0')ret.s.pop_back(); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator/(const bigint& a, const bigint& b) { bigint ret(0); bigint ans; int len = a.s.length(); rep(i, len) { ret = ret + (a.s[i] - '0'); int cnt = 0; while (ret >= b)++cnt, ret = ret - b; ans.s.push_back('0' + cnt); if (ret != 0)ret.s.push_back('0'); } rep(i, ans.s.length()) { if (ans.s[i] != '0') { ans.s.erase(ans.s.begin(), ans.s.begin() + i); break; } if (i == (int)ans.s.length() - 1) { ans = 0; } } return ans; } bigint operator%(const bigint& a, const bigint& b) { bigint ret(0); int len = a.s.length(); rep(i, len) { ret = ret + (a.s[i] - '0'); while (ret >= b)ret = ret - b; if (ret != 0 && i < len - 1)ret.s.push_back('0'); } rep(i, ret.s.size()) { if (ret.s[i] != '0' || i == ret.s.size() - 1) { ret.s.erase(ret.s.begin(), ret.s.begin() + i); break; } } return ret; } bigint multi(const bigint& a, const int& t) { bigint ret; int c = 0; per(i, a.s.length()) { c += (a.s[i] - '0') * t; ret.s.push_back('0' + (c % 10)); c /= 10; } while (c > 0) { ret.s.push_back('0' + (c % 10)); c /= 10; } while (ret != 0 && ret.s.back() == '0')ret.s.pop_back(); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator*(const bigint& a, const bigint& b) { bigint ret(0); int l = b.s.length(); rep(i, b.s.length()) { bigint u = multi(a, (b.s[l - 1 - i] - '0')); if (u != 0) { rep(j, i)u.s.push_back('0'); } ret = ret + u; } rep(i, ret.s.size()) { if (ret.s[i] != '0' || i == ret.s.size() - 1) { ret.s.erase(ret.s.begin(), ret.s.begin() + i); break; } } return ret; } bigint min(const bigint& a, const bigint& b) { if (a < b)return a; else return b; } bigint gcd(bigint a, bigint b) { if (a < b)swap(a, b); while (b > 0) { bigint r = a % b; a = b; b = r; } return a; } bigint mod_pow(bigint x, bigint n, bigint m) { bigint ret = 1; while (n != 0) { if (n % 2 != 0)ret = ret * x % m; x = x * x % m; n = n / 2; } return ret; } typedef pair bP; bool intest(bigint a, bigint d, bigint n, int s) { if (mod_pow(a, d, n) == 1)return false; rep(r, s) { bigint d_ = d; rep(i, r)d_ = d_ * 2; if (mod_pow(a, d_, n) == n - 1)return false; } return true; } bool miller_rabin_primality_test(bigint n, int t = 100) { if (n.s == "1")return false; int s = 0; bigint d = n - 1; while (d % 2 == 0) { d = d / 2; s++; } mt19937_64 mt(time(0)); rep(i, t) { ul a = mt(); ul b = mt(); bigint c(to_string(a) + to_string(b)); c = c % (n - 1); c = c + 1; if (intest(c, d, n, s))return false; } return true; } const int mn = 2001; bool isp[mn + 1]; void init() { fill(isp + 2, isp + mn + 1, true); Rep1(i, 2, mn) { if (!isp[i])continue; for (int j = 2 * i; j <= mn; j += i) { isp[j] = false; } } } bool testmincase(int n, int m) { if (isp[n])return false; vector used(n, false); queue q; q.push(0); used[0] = true; rep(i, n) { if (isp[i + 1])used[i] = true; } while (!q.empty()) { int id = q.front(); q.pop(); if (id % m) { if (!used[id - 1]) { used[id - 1] = true; q.push(id - 1); } } if ((id % m) < m - 1 && id < n - 1) { if (!used[id + 1]) { used[id + 1] = true; q.push(id + 1); } } if (id - m >= 0) { if (!used[id - m]) { used[id - m] = true; q.push(id - m); } } if (id + m < n) { if (!used[id + m]) { used[id + m] = true; q.push(id + m); } } } return used[n - 1]; } void solve() { init(); string s; cin >> s; if (s.size() <= 2) { int n = stoi(s); rep1(i, n) { if (testmincase(n, i)) { cout << i << "\n"; return; } } } else { bigint b(s); b = b - 8; if (b % 8 == 1 && miller_rabin_primality_test(b))cout << 14 << "\n"; else cout << 8 << "\n"; } } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //expr(); //int t; cin >> t; rep(i, t) //while (cin >> n >> m>>s1>>s2>>t, n) solve(); return 0; }