結果
| 問題 | No.2074 Product is Square ? |
| ユーザー |
 rniya
|
| 提出日時 | 2022-09-16 21:53:21 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 149 ms / 2,000 ms |
| コード長 | 10,318 bytes |
| コンパイル時間 | 2,107 ms |
| コンパイル使用メモリ | 211,932 KB |
| 最終ジャッジ日時 | 2025-02-07 09:22:35 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 33 |
ソースコード
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
for (size_t i = 0; i < N; i++) {
os << v[i] << (i + 1 == N ? "" : " ");
}
return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
if (i) os << ',';
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
os << '{';
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T> void mkuni(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion
namespace fast_factorize {
using u64 = uint64_t;
mt19937_64 mt(random_device{}());
u64 rng(u64 n) { return uniform_int_distribution<u64>(0, n - 1)(mt); }
struct montgomery64 {
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
static u64 mod, r, n2;
static u64 get_r() {
u64 res = mod;
for (int _ = 0; _ < 5; _++) res *= 2 - mod * res;
return -res;
}
static void set_mod(u64 m) {
assert(m < (1ULL << 62));
assert((m & 1) == 1);
mod = m;
n2 = -u128(m) % m;
r = get_r();
assert(r * mod == -1ULL);
}
static u64 get_mod() { return mod; }
static u64 reduce(const u128& x) noexcept { return (x + u128(u64(x) * r) * mod) >> 64; }
u64 v;
montgomery64() : v(0) {}
montgomery64(const i64& v) : v(reduce((u128(v) + mod) * n2)) {}
u64 value() const {
u64 res = reduce(v);
return res >= mod ? res - mod : res;
}
montgomery64& operator+=(const montgomery64& rhs) {
if (i64(v += rhs.v - (mod << 1)) < 0) v += mod << 1;
return *this;
}
montgomery64& operator-=(const montgomery64& rhs) {
if (i64(v -= rhs.v) < 0) v += mod << 1;
return *this;
}
montgomery64& operator*=(const montgomery64& rhs) {
v = reduce(u128(v) * rhs.v);
return *this;
}
montgomery64 operator+(const montgomery64& rhs) const { return montgomery64(*this) += rhs; }
montgomery64 operator-(const montgomery64& rhs) const { return montgomery64(*this) -= rhs; }
montgomery64 operator*(const montgomery64& rhs) const { return montgomery64(*this) *= rhs; }
bool operator==(const montgomery64& rhs) const {
return (v >= mod ? v - mod : v) == (rhs.v >= mod ? rhs.v - mod : rhs.v);
}
bool operator!=(const montgomery64& rhs) const {
return (v >= mod ? v - mod : v) != (rhs.v >= mod ? rhs.v - mod : rhs.v);
}
montgomery64 pow(u64 n) const {
montgomery64 self(*this), res(1);
while (n > 0) {
if (n & 1) res *= self;
self *= self;
n >>= 1;
}
return res;
}
friend istream& operator>>(istream& s, montgomery64& rhs) {
i64 v;
rhs = montgomery64{(s >> v, v)};
return s;
}
friend ostream& operator<<(ostream& s, const montgomery64& rhs) { return s << rhs.v; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
bool miller_rabin(const u64& n, const vector<u64>& as) {
if (montgomery64::get_mod() != n) montgomery64::set_mod(n);
const u64 d = (n - 1) >> __builtin_ctzll(n - 1);
const montgomery64 one(1), minus_one(n - 1);
for (u64 a : as) {
if (n <= a) break;
u64 t = d;
montgomery64 y = montgomery64(a).pow(t);
while (t != n - 1 && y != one && y != minus_one) {
y *= y;
t <<= 1;
}
if (y != minus_one && t % 2 == 0) return false;
}
return true;
}
bool is_prime(const u64& n) {
if (n == 2 || n == 3 || n == 5 || n == 7) return true;
if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
if (n < 121) return n > 1;
if (n < (1ULL << 32)) return miller_rabin(n, {2, 7, 61});
return miller_rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
u64 pollard_rho(const u64& n) {
if (~n & 1) return 2;
if (is_prime(n)) return n;
if (montgomery64::get_mod() != n) montgomery64::set_mod(n);
montgomery64 R, one(1);
auto f = [&](const montgomery64& x) { return x * x + R; };
constexpr int m = 128;
while (1) {
montgomery64 x, y, ys, q = one;
R = rng(n - 2) + 2, y = rng(n - 2) + 2;
u64 g = 1;
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 < min(m, r - k); i++) q *= x - (y = f(y));
g = gcd(q.value(), n);
}
}
if (g == n) {
do g = gcd((x - (ys = f(ys))).value(), n);
while (g == 1);
}
if (g != n) return g;
}
cerr << "failed" << '\n';
assert(false);
return -1;
}
vector<u64> inner_factorize(u64 n) {
if (n <= 1) return {};
u64 p = pollard_rho(n);
if (p == n) return {p};
auto l = inner_factorize(p);
auto r = inner_factorize(n / p);
copy(r.begin(), r.end(), back_inserter(l));
return l;
}
vector<u64> factorize(u64 n) {
auto res = inner_factorize(n);
sort(res.begin(), res.end());
return res;
}
} // namespace fast_factorize
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
void solve() {
int N;
cin >> N;
map<ll, int> mp;
for (; N--;) {
ll A;
cin >> A;
auto res = fast_factorize::factorize(A);
for (auto& x : res) mp[x]++;
}
for (auto p : mp) {
if (p.second & 1) {
cout << "No" << '\n';
return;
}
}
cout << "Yes" << '\n';
}
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int T;
cin >> T;
for (; T--;) solve();
return 0;
}