#line 1 "template/template.hpp" #include #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include #line 7 "template/io.hpp" namespace ebi { template std::ostream &operator<<(std::ostream &os, const std::pair &pa) { return os << pa.first << " " << pa.second; } template std::istream &operator>>(std::istream &os, std::pair &pa) { return os >> pa.first >> pa.second; } template std::ostream &operator<<(std::ostream &os, const std::vector &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template std::istream &operator>>(std::istream &os, std::vector &vec) { for (T &e : vec) std::cin >> e; return os; } template std::ostream &operator<<(std::ostream &os, const std::optional &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector start; std::vector elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template struct Edge { int from, to; T cost; int id; }; template struct Graph { using cost_type = E; using edge_type = Edge; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector> buff; std::vector edges; simple_csr csr; bool prepared = false; }; } // namespace ebi #line 8 "template/utility.hpp" namespace ebi { template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits::max() / 4; constexpr int INF = std::numeric_limits::max() / 2; const std::vector dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 2 "a.cpp" #line 6 "a.cpp" #include #line 10 "a.cpp" namespace fast_factorize { /* See : https://judge.yosupo.jp/submission/189742 */ // ---- gcd ---- uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) { if( x == y ) { return x; } const uint64_t a = y - x; const uint64_t b = x - y; const int n = __builtin_ctzll( b ); const uint64_t s = x < y ? a : b; const uint64_t t = x < y ? x : y; return gcd_stein_impl( s >> n, t ); } uint64_t gcd_stein( uint64_t x, uint64_t y ) { if( x == 0 ) { return y; } if( y == 0 ) { return x; } const int n = __builtin_ctzll( x ); const int m = __builtin_ctzll( y ); return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m ); } // ---- is_prime ---- uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) { uint64_t ret = 1; uint64_t acc = x; for( ; y; y >>= 1 ) { if( y & 1 ) { ret = __uint128_t(ret) * acc % mod; } acc = __uint128_t(acc) * acc % mod; } return ret; } bool miller_rabin( uint64_t n, const std::initializer_list& as ) { return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) { if( n <= a ) { return true; } int e = __builtin_ctzll( n - 1 ); uint64_t z = mod_pow( a, ( n - 1 ) >> e, n ); if( z == 1 || z == n - 1 ) { return true; } while( --e ) { z = __uint128_t(z) * z % n; if( z == 1 ) { return false; } if( z == n - 1 ) { return true; } } return false; }); } bool is_prime( uint64_t n ) { if( n == 2 ) { return true; } if( n % 2 == 0 ) { return false; } if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); } return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } ); } // ---- Montgomery ---- class Montgomery { uint64_t mod; uint64_t R; public: Montgomery( uint64_t n ) : mod(n), R(n) { for( size_t i = 0; i < 5; ++i ) { R *= 2 - mod * R; } } uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const { const __uint128_t d = __uint128_t(a) * b; const uint64_t e = c + mod + ( d >> 64 ); const uint64_t f = uint64_t(d) * R; const uint64_t g = ( __uint128_t(f) * mod ) >> 64; return e - g; } uint64_t mul( uint64_t a, uint64_t b ) const { return fma( a, b, 0 ); } }; // ---- Pollard's rho algorithm ---- uint64_t pollard_rho( uint64_t n ) { if( n % 2 == 0 ) { return 2; } const Montgomery m( n ); constexpr uint64_t C1 = 1; constexpr uint64_t C2 = 2; constexpr uint64_t M = 512; uint64_t Z1 = 1; uint64_t Z2 = 2; retry: uint64_t z1 = Z1; uint64_t z2 = Z2; for( size_t k = M; ; k *= 2 ) { const uint64_t x1 = z1 + n; const uint64_t x2 = z2 + n; for( size_t j = 0; j < k; j += M ) { const uint64_t y1 = z1; const uint64_t y2 = z2; uint64_t q1 = 1; uint64_t q2 = 2; z1 = m.fma( z1, z1, C1 ); z2 = m.fma( z2, z2, C2 ); for( size_t i = 0; i < M; ++i ) { const uint64_t t1 = x1 - z1; const uint64_t t2 = x2 - z2; z1 = m.fma( z1, z1, C1 ); z2 = m.fma( z2, z2, C2 ); q1 = m.mul( q1, t1 ); q2 = m.mul( q2, t2 ); } q1 = m.mul( q1, x1 - z1 ); q2 = m.mul( q2, x2 - z2 ); const uint64_t q3 = m.mul( q1, q2 ); const uint64_t g3 = gcd_stein( n, q3 ); if( g3 == 1 ) { continue; } if( g3 != n ) { return g3; } const uint64_t g1 = gcd_stein( n, q1 ); const uint64_t g2 = gcd_stein( n, q2 ); const uint64_t C = g1 != 1 ? C1 : C2; const uint64_t x = g1 != 1 ? x1 : x2; uint64_t z = g1 != 1 ? y1 : y2; uint64_t g = g1 != 1 ? g1 : g2; if( g == n ) { do { z = m.fma( z, z, C ); g = gcd_stein( n, x - z ); } while( g == 1 ); } if( g != n ) { return g; } Z1 += 2; Z2 += 2; goto retry; } } } void factorize_impl( uint64_t n, std::vector& ret ) { if( n <= 1 ) { return; } if( is_prime( n ) ) { ret.push_back( n ); return; } const uint64_t p = pollard_rho( n ); factorize_impl( p, ret ); factorize_impl( n / p, ret ); } std::vector factorize( uint64_t n ) { std::vector ret; factorize_impl( n, ret ); std::sort( ret.begin(), ret.end() ); return ret; } } // namespace fast_factorize namespace noya2 { std::vector> factorize(long long n){ std::vector> ans; auto ps = fast_factorize::factorize(n); int sz = ps.size(); for (int l = 0, r = 0; l < sz; l = r){ while (r < sz && ps[l] == ps[r]) r++; ans.emplace_back(ps[l], r-l); } return ans; } std::vector divisors(long long n){ auto ps = fast_factorize::factorize(n); int sz = ps.size(); std::vector ans = {1}; for (int l = 0, r = 0; l < sz; l = r){ while (r < sz && ps[l] == ps[r]) r++; int e = r - l; int len = ans.size(); ans.reserve(len*(e+1)); long long mul = ps[l]; while (true){ for (int i = 0; i < len; i++){ ans.emplace_back(ans[i]*mul); } if (--e == 0) break; mul *= ps[l]; } } return ans; } std::vector divisors(const std::vector> &pes){ std::vector ans = {1}; for (auto [p, e] : pes){ int len = ans.size(); ans.reserve(len*(e+1)); long long mul = p; while (true){ for (int i = 0; i < len; i++){ ans.emplace_back(ans[i]*mul); } if (--e == 0) break; mul *= p; } } return ans; } } // namespace noya2 namespace ebi { void main_() { i64 n; std::cin >> n; auto a = noya2::divisors(n); i64 ans = 0; for(auto x: a) { ans += x; if(ans > 2 * n) { std::cout << "No\n"; return; } } std::cout << (ans == 2 * n ? "Yes" : "No") << '\n'; } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }