結果
| 問題 |
No.2795 Perfect Number
|
| コンテスト | |
| ユーザー |
 dekatin
|
| 提出日時 | 2024-06-29 12:41:49 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 10 ms / 2,000 ms |
| コード長 | 25,151 bytes |
| コンパイル時間 | 5,733 ms |
| コンパイル使用メモリ | 307,996 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-06-29 12:41:57 |
| 合計ジャッジ時間 | 7,054 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 35 |
ソースコード
#line 1 "lib/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define int long long
using ll = long long;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
#define str string
using db = long double;
template <class T> constexpr T infty = 0;
template <> constexpr int32_t infty<int32_t> = 1'000'000'000;
template <> constexpr ll infty<ll> = ll(infty<int32_t>) * infty<int32_t> * 2;
template <> constexpr u32 infty<u32> = infty<int32_t>;
template <> constexpr u64 infty<u64> = infty<ll>;
template <> constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <> constexpr double infty<double> = infty<ll>;
template <> constexpr long double infty<long double> = infty<ll>;
using pi = pair<int, int>;
using pd = pair<db, db>;
#define mp make_pair
#define f first
#define s second
#define tcT template <class T
#define tcTU tcT, class U
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
using vi = V<int>;
using vb = V<bool>;
using vd = V<db>;
using vs = V<string>;
using vpi = V<pi>;
using vpd = V<pd>;
tcT > using pqg = priority_queue<T, vector<T>, greater<T>>;
#define sz(x) (int)((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
tcT > T POP(V<T>& a) {
T res = a.bk;
a.pop_back();
return res;
}
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T>& a, const T& b) { return (int)(lb(all(a), b) - bg(a)); }
tcT > int upb(V<T>& a, const T& b) { return (int)(ub(all(a), b) - bg(a)); }
#define each(a, x) for (auto& a : x)
#define rep1(a) for (ll _ = 0; _ < (ll)(a); ++_)
#define rep2(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define rep3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (c))
#define cut4(a, b, c, d, e, ...) e
#define rep(...) cut4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define per1(n) for (ll _ = ((ll)n) - 1; _ >= 0; --_)
#define per2(i, n) for (ll i = ((ll)n) - 1; i >= 0; --i)
#define per3(i, a, b) for (ll i = ((ll)b) - 1; i >= (ll)(a); --i)
#define per4(i, a, b, c) for (ll i = ((ll)b) - 1; i >= (ll)(a); i -= (c))
#define per(...) cut4(__VA_ARGS__, per4, per3, per2, per1)(__VA_ARGS__)
#define rep_subset(i, s) \
for (ll i = (s); i >= 0; i = (i == 0 ? -1 : (i - 1) & (s)))
const int dx[8]{1, 0, -1, 0, 1, 1, -1, -1}, dy[8]{0, 1, 0, -1, 1, -1, 1, -1};
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int topbit(int x) { return x == 0 ? 0 : 63 - __builtin_clzll(x); }
constexpr int lowbit(int x) { return x == 0 ? 0 : __builtin_ctzll(x); }
constexpr int isp2(int x) { return x && (x & -x) == x; }
constexpr int mask(int x) { return (1ll << x) - 1; }
int cdiv(int a, int b) { return a / b + ((a ^ b) > 0 && a % b); }
int fdiv(int a, int b) { return a / b - ((a ^ b) < 0 && a % b); }
int root2(int x) {
int res = sqrtl(x) + 2;
while (res * res > x) --res;
return res;
}
tcT > bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
tcT > bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
tcTU > T fstTrue(T lo, T hi, U f) {
++hi;
assert(lo <= hi);
while (lo < hi) {
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
--lo;
assert(lo <= hi);
while (lo < hi) {
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void Unique(vector<T>& v) {
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcT > V<T> prefSum(V<T>& a, int off = 1) {
int N = sz(a);
V<T> ret(N + 1);
rep(i, N) ret[i + 1] = ret[i] + a[i];
if (off == 0) ret.erase(ret.begin());
return ret;
}
tcT > V<T> sufSum(const V<T>& a) {
V<T> ret = a;
per(i, sz(ret) - 1) ret[i] += ret[i + 1];
return ret;
}
// sorted[i] = v[idx[i]]
tcT > vi sortedIdx(const V<T>& v) {
vi ret(sz(v));
iota(all(ret), 0);
sort(all(ret), [&](int i, int j) { return v[i] < v[j]; });
return ret;
}
tcT > vi rearrange(const V<T>& v, const vi& idx) {
vi ret(sz(v));
rep(i, sz(v)) ret[i] = v[idx[i]];
return ret;
}
// ? = -1
tcT > vi str_to_vi(const str& S, T first_char) {
vi A(sz(S));
rep(i, sz(S)) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
tcT > vi Cnt(const V<T>& v, int mx) {
vi cnt(mx + 1);
each(x, v) cnt[x]++;
return cnt;
}
tcT > T Sum(const V<T>& v) {
T ret = 0;
each(x, v) ret += x;
return ret;
}
tcT > T Max(const V<T>& v) { return *max_element(all(v)); }
tcT > T Min(const V<T>& v) { return *min_element(all(v)); }
tcT > int MaxIdx(const V<T>& v) { return max_element(all(v)) - bg(v); }
tcT > int MinIdx(const V<T>& v) { return min_element(all(v)) - bg(v); }
tcT > V<T> Transpose(const V<T>& v) {
using U = typename T::value_type;
if (v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
tcT > V<T> Rotate(const V<T>& v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[j][H - 1 - i] = v[i][j];
} else {
res[W - 1 - j][i] = v[i][j];
}
}
}
return res;
}
inline namespace IO {
#define SFINAE(x, ...) \
template <class, class = void> struct x : std::false_type {}; \
template <class T> struct x<T, std::void_t<__VA_ARGS__>> : std::true_type {}
SFINAE(DefaultI, decltype(std::cin >> std::declval<T&>()));
SFINAE(DefaultO, decltype(std::cout << std::declval<T&>()));
SFINAE(IsTuple, typename std::tuple_size<T>::type);
SFINAE(Iterable, decltype(std::begin(std::declval<T>())));
template <auto& is> struct Reader {
template <class T> void Impl(T& t) {
if constexpr (DefaultI<T>::value)
is >> t;
else if constexpr (Iterable<T>::value) {
for (auto& x : t) Impl(x);
} else if constexpr (IsTuple<T>::value) {
std::apply([this](auto&... args) { (Impl(args), ...); }, t);
} else
static_assert(IsTuple<T>::value, "No matching type for read");
}
template <class... Ts> void read(Ts&... ts) { ((Impl(ts)), ...); }
};
template <class... Ts> void re(Ts&... ts) { Reader<cin>{}.read(ts...); }
#define def(t, args...) \
t args; \
re(args);
#define defi(args...) def(int, args)
#define defs(args...) def(str, args)
#define defd(args...) def(db, args)
#define defv(t, name, size) \
V<t> name(size); \
re(name);
#define defvi1(name, size) \
vi name(size); \
re(name);
#define defvi2(name, size, offset) \
vi name(size + offset); \
rep(i, offset, size + offset) re(name[i]);
#define cut3(a, b, c, d, ...) d
#define defvi(...) cut3(__VA_ARGS__, defvi2, defvi1)(__VA_ARGS__)
#define re2(s, t) \
for (int i = 0; i < sz(s); i++) { \
re(s[i], t[i]); \
}
#define re3(s, t, u) \
for (int i = 0; i < sz(s); i++) { \
re(s[i], t[i], u[i]); \
}
#define re4(s, t, u, v) \
for (int i = 0; i < sz(s); i++) { \
re(s[i], t[i], u[i], v[i]); \
}
template <auto& os, bool debug, bool print_nd> struct Writer {
string comma() const { return debug ? "," : ""; }
template <class T> constexpr char Space(const T&) const {
return print_nd && (Iterable<T>::value or IsTuple<T>::value) ? '\n'
: ' ';
}
template <class T> void Impl(T const& t) const {
if constexpr (DefaultO<T>::value)
os << t;
else if constexpr (Iterable<T>::value) {
if (debug) os << '{';
int i = 0;
for (auto&& x : t)
((i++) ? (os << comma() << Space(x), Impl(x)) : Impl(x));
if (debug) os << '}';
} else if constexpr (IsTuple<T>::value) {
if (debug) os << '(';
std::apply(
[this](auto const&... args) {
int i = 0;
(((i++) ? (os << comma() << " ", Impl(args)) : Impl(args)),
...);
},
t);
if (debug) os << ')';
} else
static_assert(IsTuple<T>::value, "No matching type for print");
}
template <class T> void ImplWrapper(T const& t) const { Impl(t); }
template <class... Ts> void print(Ts const&... ts) const {
((Impl(ts)), ...);
}
template <class F, class... Ts>
void print_with_sep(const std::string& sep,
F const& f,
Ts const&... ts) const {
ImplWrapper(f), ((os << sep, ImplWrapper(ts)), ...), os << '\n';
}
void print_with_sep(const std::string&) const { os << '\n'; }
};
template <class... Ts> void pr(Ts const&... ts) {
Writer<cout, false, true>{}.print(ts...);
}
template <class... Ts> void ps(Ts const&... ts) {
Writer<cout, false, true>{}.print_with_sep(" ", ts...);
}
} // namespace IO
inline namespace Debug {
template <typename... Args> void err(Args... args) {
Writer<cerr, true, false>{}.print_with_sep(" | ", args...);
}
void err_prefix(string func, int line, string args) {
cerr << func << ":" << line << " - " << "[" << args << "] = ";
}
#ifdef LOCAL
#define dbg(args...) err_prefix(__FUNCTION__, __LINE__, #args), err(args)
#else
#define dbg(...)
#endif
void setIO() {
cin.tie(0)->sync_with_stdio(0);
cout << fixed << setprecision(12);
}
} // namespace Debug
void YES(bool t = 1) { ps(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { ps(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { ps(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
namespace std {
template <class Fun> class y_combinator_result {
Fun fun_;
public:
template <class T>
explicit y_combinator_result(T&& fun) : fun_(std::forward<T>(fun)) {}
template <class... Args> decltype(auto) operator()(Args&&... args) {
return fun_(std::ref(*this), std::forward<Args>(args)...);
}
};
template <class Fun> decltype(auto) fun(Fun&& fun) {
return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
} // usage : fun([&](auto dfs, int u, int p) -> void ...
} // namespace std
#line 4 "lib/fast-factorize.hpp"
using namespace std;
#line 2 "lib/rng.hpp"
#line 2 "lib/internal-seed.hpp"
using namespace std;
namespace internal {
unsigned long long non_deterministic_seed() {
unsigned long long m =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
m ^= 9845834732710364265uLL;
m ^= m << 24, m ^= m >> 31, m ^= m << 35;
return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }
// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#ifdef LOCAL
return deterministic_seed();
#else
return non_deterministic_seed();
#endif
}
} // namespace internal
#line 4 "lib/rng.hpp"
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x = internal::seed();
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % u64(r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % u64(r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
sort(begin(ret), end(ret));
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
assert(l < r);
return l + rnd() * (r - l);
}
template <typename T> void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "lib/miller-rabin.hpp"
using namespace std;
#line 2 "lib/arbitrary-montgomery-modint.hpp"
using namespace std;
template <typename Int, typename UInt, typename Long, typename ULong, int32_t id>
struct ArbitraryLazyMontgomeryModIntBase {
using mint = ArbitraryLazyMontgomeryModIntBase;
inline static UInt mod;
inline static UInt r;
inline static UInt n2;
static constexpr int32_t bit_length = sizeof(UInt) * 8;
static UInt get_r() {
UInt ret = mod;
while (mod * ret != 1) ret *= UInt(2) - mod * ret;
return ret;
}
static void set_mod(UInt m) {
assert(m < (UInt(1u) << (bit_length - 2)));
assert((m & 1) == 1);
mod = m, n2 = -ULong(m) % m, r = get_r();
}
UInt a;
ArbitraryLazyMontgomeryModIntBase() : a(0) {}
ArbitraryLazyMontgomeryModIntBase(const Long& b)
: a(reduce(ULong(b % mod + mod) * n2)){};
static UInt reduce(const ULong& b) {
return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length;
}
mint& operator+=(const mint& b) {
if (Int(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint& operator-=(const mint& b) {
if (Int(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint& operator*=(const mint& b) {
a = reduce(ULong(a) * b.a);
return *this;
}
mint& operator/=(const mint& b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint& b) const { return mint(*this) += b; }
mint operator-(const mint& b) const { return mint(*this) -= b; }
mint operator*(const mint& b) const { return mint(*this) *= b; }
mint operator/(const mint& b) const { return mint(*this) /= b; }
bool operator==(const mint& b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const mint& b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
mint operator-() const { return mint(0) - mint(*this); }
mint operator+() const { return mint(*this); }
mint pow(ULong n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul, n >>= 1;
}
return ret;
}
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
Long t;
is >> t;
b = ArbitraryLazyMontgomeryModIntBase(t);
return (is);
}
mint inverse() const {
Int x = get(), y = get_mod(), u = 1, v = 0;
while (y > 0) {
Int t = x / y;
swap(x -= t * y, y);
swap(u -= t * v, v);
}
return mint{u};
}
UInt get() const {
UInt ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static UInt get_mod() { return mod; }
};
// id に適当な乱数を割り当てて使う
template <int32_t id>
using ArbitraryLazyMontgomeryModInt =
ArbitraryLazyMontgomeryModIntBase<int32_t,
uint32_t,
long long,
unsigned long long,
id>;
template <int32_t id>
using ArbitraryLazyMontgomeryModInt64bit =
ArbitraryLazyMontgomeryModIntBase<long long,
unsigned long long,
__int128_t,
__uint128_t,
id>;
#line 1 "lib/internal-type-traits.hpp"
#include <type_traits>
using namespace std;
namespace internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type,
false_type>::type;
template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type,
false_type>::type;
template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type,
false_type>::type;
#define ENABLE_VALUE(x) \
template <typename T> constexpr bool x##_v = x<T>::value;
ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE
#define ENABLE_HAS_TYPE(var) \
template <class, class = void> struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T> constexpr auto has_##var##_v = has_##var<T>::value;
#define ENABLE_HAS_VAR(var) \
template <class, class = void> struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T> constexpr auto has_##var##_v = has_##var<T>::value;
} // namespace internal
#line 2 "lib/internal-math.hpp"
namespace internal {
#line 6 "lib/internal-math.hpp"
using namespace std;
// a mod p
template <typename T> T safe_mod(T a, T p) {
a %= p;
if constexpr (is_broadly_signed_v<T>) {
if (a < 0) a += p;
}
return a;
}
// 返り値：pair(g, x)
// s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
template <typename T> pair<T, T> inv_gcd(T a, T p) {
static_assert(is_broadly_signed_v<T>);
a = safe_mod(a, p);
if (a == 0) return {p, 0};
T b = p, x = 1, y = 0;
while (a != 0) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
if (y < 0) y += p / b;
return {b, y};
}
// 返り値 : a^{-1} mod p
// gcd(a, p) != 1 が必要
template <typename T> T inv(T a, T p) {
static_assert(is_broadly_signed_v<T>);
a = safe_mod(a, p);
T b = p, x = 1, y = 0;
while (a != 0) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
assert(b == 1);
return y < 0 ? y + p : y;
}
// T : 底の型
// U : T*T がオーバーフローしない かつ 指数の型
template <typename T, typename U> T modpow(T a, U n, T p) {
a = safe_mod(a, p);
T ret = 1 % p;
while (n != 0) {
if (n % 2 == 1) ret = U(ret) * a % p;
a = U(a) * a % p;
n /= 2;
}
return ret;
}
// 返り値 : pair(rem, mod)
// 解なしのときは {0, 0} を返す
template <typename T> pair<T, T> crt(const vector<T>& r, const vector<T>& m) {
static_assert(is_broadly_signed_v<T>);
assert(r.size() == m.size());
int n = (int)(r.size());
T r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
T r1 = safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) swap(r0, r1), swap(m0, m1);
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
auto [g, im] = inv_gcd(m0, m1);
T u1 = m1 / g;
if ((r1 - r0) % g) return {0, 0};
T x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
} // namespace internal
#line 6 "lib/miller-rabin.hpp"
namespace fast_factorize {
template <typename T, typename U> bool miller_rabin(const T& n, vector<T> ws) {
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
T d = n - 1;
while (d % 2 == 0) d /= 2;
U e = 1, rev = n - 1;
for (T w : ws) {
if (w % n == 0) continue;
T t = d;
U y = internal::modpow<T, U>(w, t, n);
while (t != n - 1 && y != e && y != rev) y = y * y % n, t *= 2;
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool miller_rabin_u64(unsigned long long n) {
return miller_rabin<unsigned long long, __uint128_t>(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
template <typename mint>
bool miller_rabin(unsigned long long n, vector<unsigned long long> ws) {
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
if (mint::get_mod() != n) mint::set_mod(n);
unsigned long long d = n - 1;
while (~d & 1) d >>= 1;
mint e = 1, rev = n - 1;
for (unsigned long long w : ws) {
if (w % n == 0) continue;
unsigned long long t = d;
mint y = mint(w).pow(t);
while (t != n - 1 && y != e && y != rev) y *= y, t *= 2;
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool is_prime(unsigned long long n) {
using mint32 = ArbitraryLazyMontgomeryModInt<96229631>;
using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>;
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
if (n < (1uLL << 30)) {
return miller_rabin<mint32>(n, {2, 7, 61});
} else if (n < (1uLL << 62)) {
return miller_rabin<mint64>(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
} else {
return miller_rabin_u64(n);
}
}
} // namespace fast_factorize
using fast_factorize::is_prime;
#line 8 "lib/fast-factorize.hpp"
namespace fast_factorize {
using u64 = uint64_t;
template <typename mint, typename T> T pollard_rho(T n) {
if (~n & 1) return 2;
if (is_prime(n)) return n;
if (mint::get_mod() != n) mint::set_mod(n);
mint R, one = 1;
auto f = [&](mint x) { return x * x + R; };
auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
while (1) {
mint x, y, ys, q = one;
R = rnd_(), y = rnd_();
T g = 1;
constexpr int m = 128;
for (int r = 1; g == 1; r <<= 1) {
x = y;
for (int i = 0; i < r; ++i) y = f(y);
for (int k = 0; g == 1 && k < r; k += m) {
ys = y;
for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = gcd(q.get(), n);
}
}
if (g == n) do
g = gcd((x - (ys = f(ys))).get(), n);
while (g == 1);
if (g != n) return g;
}
exit(1);
}
using i64 = long long;
vector<i64> inner_factorize(u64 n) {
using mint32 = ArbitraryLazyMontgomeryModInt<452288976>;
using mint64 = ArbitraryLazyMontgomeryModInt64bit<401243123>;
if (n <= 1) return {};
u64 p;
if (n <= (1LL << 30)) {
p = pollard_rho<mint32, uint32_t>(n);
} else if (n <= (1LL << 62)) {
p = pollard_rho<mint64, uint64_t>(n);
} else {
exit(1);
}
if (p == n) return {i64(p)};
auto l = inner_factorize(p);
auto r = inner_factorize(n / p);
copy(begin(r), end(r), back_inserter(l));
return l;
}
vector<i64> factorize(u64 n) {
auto ret = inner_factorize(n);
sort(begin(ret), end(ret));
return ret;
}
map<i64, i64> factor_count(u64 n) {
map<i64, i64> mp;
for (auto& x : factorize(n)) mp[x]++;
return mp;
}
vector<i64> divisors(u64 n) {
if (n == 0) return {};
vector<pair<i64, i64>> v;
for (auto& p : factorize(n)) {
if (v.empty() || v.back().first != p) {
v.emplace_back(p, 1);
} else {
v.back().second++;
}
}
vector<i64> ret;
auto f = [&](auto rc, int i, i64 x) -> void {
if (i == (int)v.size()) {
ret.push_back(x);
return;
}
rc(rc, i + 1, x);
for (int j = 0; j < v[i].second; j++) rc(rc, i + 1, x *= v[i].first);
};
f(f, 0, 1);
sort(begin(ret), end(ret));
return ret;
}
} // namespace fast_factorize
using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
#line 3 "main.cpp"
void solve(int tc) {
defi(n);
Yes(2 * n == Sum(divisors(n)));
}
signed main() {
setIO();
int TC = 1;
// re(TC);
rep(i, 1, TC + 1) solve(i);
}