#include #include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } // from https://judge.yosupo.jp/submission/84154 using u64 = unsigned long long; using u32 = unsigned; u32 modpow(u32 a, u32 n, u32 p){ u32 r = 1; for(; n; n >>= 1){ if(n & 1) r = (u64) r * a % p; a = (u64) a * a % p; } return r; } bool is_square(u32 n, u32 p){ n %= p; return n == 0 || modpow(n, (p-1)/2, p) == 1; } u32 sqrt_mod(u32 n, u32 p){ u32 a = 2; while(is_square(((u64) a * a + p - n) % p, p)){ a++; } a = 2 * a % p; u64 s = 1; u64 t = p - a; u64 u = p - a; u64 v = n; u32 m = (p+1)/2; while(m) { if(m & 1){ s = ((p - s) * u + t) % p; t = t * v % p; } else { t = (s * v + (p - t) * u) % p; } u = (2 * v + (p - u) * u) % p; v = v * v % p; m /= 2; } return s; } using mint = atcoder::modint; ostream& operator<<(ostream& os, const mint& m){ os << m.val(); return os; } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; int p; cin >> p; mint::set_mod(p); mint k = (mint(p)-1)/2; mint x = k*k+4*k+2; mint s = mint(9)-4*x; if(!is_square(s.val(), p)){ cout << "NO" << endl; return 0; } cout << "YES" << endl; // auto ans = mint(sqrt_mod(s.val(), p)); // if(ans*ans == s){ // }else{ // cout << "NO" << endl; // } }