#include using namespace std; using ll = long long; const int INF = (int)1e9 + 1001010; const ll llINF = (long long)4e18 + 22000020; const string endn = "\n"; template inline auto vector2(size_t i, size_t j, const T &init = T()) {return vector(i, vector(j, init));} const string ELEM_SEPARATION = " ", VEC_SEPARATION = endn; template istream& operator >>(istream &i, vector &A) {for(auto &I : A) {i >> I;} return i;} template ostream& operator <<(ostream &o, const vector &A) {int i=A.size(); for(const auto &I : A){o << I << (--i ? ELEM_SEPARATION : "");} return o;} template ostream& operator <<(ostream &o, const vector> &A) {int i=A.size(); for(const auto &I : A){o << I << (--i ? VEC_SEPARATION : "");} return o;} template vector& operator ++(vector &A, int n) {for(auto &I : A) {I++;} return A;} template vector& operator --(vector &A, int n) {for(auto &I : A) {I--;} return A;} template bool chmax(T &a, const U &b) {return ((a < b) ? (a = b, true) : false);} template bool chmin(T &a, const U &b) {return ((a > b) ? (a = b, true) : false);} ll floor(ll a, ll b){if (b < 0) a = -a, b = -b; if(a >= 0) return a / b; else return (a + 1) / b - 1;} ll ceil(ll a, ll b){if (b < 0) a = -a, b = -b; if(a > 0) return (a - 1) / b + 1; else return a / b;} ll bit(unsigned long long val, unsigned long long digit){return (val >> digit) & 1;} #ifdef DEBUG #include #else #define debug(...) #endif // ================================== ここまでテンプレ ================================== //------------------------------// // Prime Functions //------------------------------// // montgomery modint (MOD < 2^62, MOD is odd) struct MontgomeryModInt64 { using mint = MontgomeryModInt64; using u64 = uint64_t; using u128 = __uint128_t; // static menber static u64 MOD; static u64 INV_MOD; // INV_MOD * MOD ≡ 1 (mod 2^64) static u64 T128; // 2^128 (mod MOD) // inner value u64 val; // constructor MontgomeryModInt64() : val(0) { } MontgomeryModInt64(long long v) : val(reduce((u128(v) + MOD) * T128)) { } u64 get() const { u64 res = reduce(val); return res >= MOD ? res - MOD : res; } // mod getter and setter static u64 get_mod() { return MOD; } static void set_mod(u64 mod) { assert(mod < (1LL << 62)); assert((mod & 1)); MOD = mod; T128 = -u128(mod) % mod; INV_MOD = get_inv_mod(); } static u64 get_inv_mod() { u64 res = MOD; for (int i = 0; i < 5; ++i) res *= 2 - MOD * res; return res; } static u64 reduce(const u128 &v) { return (v + u128(u64(v) * u64(-INV_MOD)) * MOD) >> 64; } // arithmetic operators mint operator + () const { return mint(*this); } mint operator - () const { return mint() - mint(*this); } mint operator + (const mint &r) const { return mint(*this) += r; } mint operator - (const mint &r) const { return mint(*this) -= r; } mint operator * (const mint &r) const { return mint(*this) *= r; } mint operator / (const mint &r) const { return mint(*this) /= r; } mint& operator += (const mint &r) { if ((val += r.val) >= 2 * MOD) val -= 2 * MOD; return *this; } mint& operator -= (const mint &r) { if ((val += 2 * MOD - r.val) >= 2 * MOD) val -= 2 * MOD; return *this; } mint& operator *= (const mint &r) { val = reduce(u128(val) * r.val); return *this; } mint& operator /= (const mint &r) { *this *= r.inv(); return *this; } mint inv() const { return pow(MOD - 2); } mint pow(u128 n) const { mint res(1), mul(*this); while (n > 0) { if (n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } // other operators bool operator == (const mint &r) const { return (val >= MOD ? val - MOD : val) == (r.val >= MOD ? r.val - MOD : r.val); } bool operator != (const mint &r) const { return (val >= MOD ? val - MOD : val) != (r.val >= MOD ? r.val - MOD : r.val); } mint& operator ++ () { ++val; if (val >= MOD) val -= MOD; return *this; } mint& operator -- () { if (val == 0) val += MOD; --val; return *this; } mint operator ++ (int) { mint res = *this; ++*this; return res; } mint operator -- (int) { mint res = *this; --*this; return res; } friend istream& operator >> (istream &is, mint &x) { long long t; is >> t; x = mint(t); return is; } friend ostream& operator << (ostream &os, const mint &x) { return os << x.get(); } friend mint pow(const mint &r, long long n) { return r.pow(n); } friend mint inv(const mint &r) { return r.inv(); } }; typename MontgomeryModInt64::u64 MontgomeryModInt64::MOD, MontgomeryModInt64::INV_MOD, MontgomeryModInt64::T128; // Miller-Rabin bool MillerRabin(long long N, vector A) { using mint = MontgomeryModInt64; mint::set_mod(N); long long s = 0, d = N - 1; while (d % 2 == 0) { ++s; d >>= 1; } for (auto a : A) { if (N <= a) return true; mint x = mint(a).pow(d); if (x != 1) { long long t; for (t = 0; t < s; ++t) { if (x == N - 1) break; x *= x; } if (t == s) return false; } } return true; } bool is_prime(long long N) { if (N <= 1) return false; else if (N == 2) return true; else if (N % 2 == 0) return false; else if (N < 4759123141LL) return MillerRabin(N, {2, 7, 61}); else return MillerRabin(N, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}); } // Pollard's Rho unsigned int xor_shift_rng() { static unsigned int tx = 123456789, ty=362436069, tz=521288629, tw=88675123; unsigned int tt = (tx^(tx<<11)); tx = ty, ty = tz, tz = tw; return ( tw=(tw^(tw>>19))^(tt^(tt>>8)) ); } long long pollard(long long N) { if (N % 2 == 0) return 2; if (is_prime(N)) return N; using mint = MontgomeryModInt64; mint::set_mod(N); long long step = 0; while (true) { mint r = xor_shift_rng(); // random r auto f = [&](mint x) -> mint { return x * x + r; }; mint x = ++step, y = f(x); while (true) { long long p = gcd((y - x).get(), N); if (p == 0 || p == N) break; if (p != 1) return p; x = f(x); y = f(f(y)); } } } vector prime_factorize(long long N) { if (N == 1) return {}; long long p = pollard(N); if (p == N) return {p}; vector left = prime_factorize(p); vector right = prime_factorize(N / p); left.insert(left.end(), right.begin(), right.end()); sort(left.begin(), left.end()); return left; } #include using i128 = boost::multiprecision::int128_t; using i256 = boost::multiprecision::int256_t; using i512 = boost::multiprecision::int512_t; using i1024 = boost::multiprecision::int1024_t; using iINF = boost::multiprecision::cpp_int; #include using d30 = boost::multiprecision::number>; using d50 = boost::multiprecision::cpp_dec_float_50; using d100 = boost::multiprecision::cpp_dec_float_100; i128 powll(i128 base, i128 exponent){ i128 ret = 1; while(exponent > 0){ if(exponent & 1) ret = ret * base; base = base * base; exponent >>= 1; } return ret; } int main(int argc, char *argv[]){ ios::sync_with_stdio(false); cin.tie(nullptr); ll n; cin >> n; vector factors = prime_factorize(n); map fac_pow; for(int i = 0; i < factors.size(); i++){ fac_pow[factors[i]]++; } i128 ans = 1; for(auto [r, n] : fac_pow){ i128 sum = (powll(r, n+1) - 1) / (r - 1); debug(r, n, sum); ans *= sum; } if(ans == 2*n) cout << "Yes" << endl; else cout << "No" << endl; return 0; }