#include using namespace std; using VS = vector; using LL = long long; using VI = vector; using VVI = vector; using PII = pair; using PLL = pair; using VL = vector; using VVL = vector; #define ALL(a) begin((a)),end((a)) #define RALL(a) (a).rbegin(), (a).rend() #define SZ(a) int((a).size()) #define SORT(c) sort(ALL((c))) #define RSORT(c) sort(RALL((c))) #define UNIQ(c) (c).erase(unique(ALL((c))), end((c))) #define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++) #define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--) #define debug(x) cerr << #x << ": " << x << endl const int INF = 1e9; const LL LINF = 1e16; const LL MOD = 1000000007; const double PI = acos(-1.0); int DX[8] = { 0, 0, 1, -1, 1, 1, -1, -1 }; int DY[8] = { 1, -1, 0, 0, 1, -1, 1, -1 }; /* ----- 2018/09/30 Problem: yukicoder 308 / Link: http://yukicoder.me/problems/no/308 ----- */ /* ------問題------ -----問題ここまで----- */ /* -----解説等----- オーバーフロー… ----解説ここまで---- */ using LLL = __int128; __int128 parse(string &s) { __int128 ret = 0; for (int i = 0; i < (int)s.length(); i++) if (isdigit(s[i])) ret = 10 * ret + s[i] - '0'; if (s[0] == '-')ret = -ret; return ret; } std::istream &operator>>(std::istream &is, __int128 &value) { string s; cin >> s; value = parse(s); return is; } vector make_prime(LL N) { vector prime(N + 1, 1); prime[0] = prime[1] = 0; for (int i = 2; i <= N; i++) { if (prime[i]) { for (int j = i * 2; j <= N; j += i) prime[j] = 0; } } return prime; } LLL mul(const LLL a, const LLL b, const LLL mod) { if (b == 0) { return 0; } if (b % 2 == 1) { return (mul(a, b - 1, mod) + a) % mod; } else { const LLL pp = mul(a, b / 2, mod); return (pp + pp) % mod; } } LLL power(const LLL a, const LLL n, const LLL mod) { if (n == 0) { return 1; } if (n % 2 == 1) { return mul(power(a, n - 1, mod), a, mod); } else { const LLL aa = power(a, n / 2, mod); return mul(aa, aa, mod); } } int main() { cin.tie(0); ios_base::sync_with_stdio(false); LLL N; cin >> N; int ans = 0; if (N <= 1000) { VI is_prime = make_prime(N + 1); for (int w = 3; ; w++) { VI masu(N + 1, 0); masu[1] = 1; queueq; q.push(1); #define IN(a,b,c) (a<=b&&b ds({ -w,w,-1,1 }); while (!q.empty()) { int pos = q.front(); q.pop(); FOR(k, 0, 4) { if (k == 3 && pos%w == 0)continue; if (k == 2 && pos%w == 1)continue; int nx = pos + ds[k]; if (IN(1, nx, N + 1) && !masu[nx] && !is_prime[nx]) { masu[nx] = 1; q.push(nx); } } } if (masu[N]) { ans = w; break; } } } else { auto f = [](LLL n) { if (n == 1) { return 0; } LLL s = 0, d = n - 1; while (!(d & 1))s++, d >>= 1; mt19937_64 rand_src(random_device{}()); FOR(i, 0, 100) { const LLL a = (rand_src() % (n - 2)) + 1; if (power(a, n - 1, n) != 1) { return 0; } LLL num = power(a, d, n); if (num != 1) { bool comp = true; FOR(_, 0, s) { if (num == n - 1) { comp = 0; break; } num = mul(num, num, n); } if (comp) return 0; } } return 1; }; if (N % 8 == 1) { // if N-8 prime : ans = 14 if (f(N - 8))ans = 14; else ans = 8; } else { ans = 8; } } cout << ans << "\n"; return 0; }