結果

問題 No.2074 Product is Square ?
ユーザー ruthenruthen
提出日時 2022-09-16 23:04:18
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 169 ms / 2,000 ms
コード長 11,156 bytes
コンパイル時間 3,049 ms
コンパイル使用メモリ 235,940 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-23 16:32:09
合計ジャッジ時間 6,164 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
このコードへのチャレンジ（β）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,376 KB
testcase_01 AC 40 ms
4,376 KB
testcase_02 AC 40 ms
4,380 KB
testcase_03 AC 39 ms
4,380 KB
testcase_04 AC 40 ms
4,376 KB
testcase_05 AC 41 ms
4,376 KB
testcase_06 AC 41 ms
4,380 KB
testcase_07 AC 41 ms
4,380 KB
testcase_08 AC 41 ms
4,376 KB
testcase_09 AC 39 ms
4,380 KB
testcase_10 AC 39 ms
4,380 KB
testcase_11 AC 15 ms
4,376 KB
testcase_12 AC 43 ms
4,380 KB
testcase_13 AC 162 ms
4,380 KB
testcase_14 AC 29 ms
4,380 KB
testcase_15 AC 15 ms
4,376 KB
testcase_16 AC 45 ms
4,380 KB
testcase_17 AC 169 ms
4,380 KB
testcase_18 AC 31 ms
4,376 KB
testcase_19 AC 14 ms
4,380 KB
testcase_20 AC 43 ms
4,376 KB
testcase_21 AC 161 ms
4,380 KB
testcase_22 AC 27 ms
4,376 KB
testcase_23 AC 15 ms
4,380 KB
testcase_24 AC 45 ms
4,380 KB
testcase_25 AC 165 ms
4,376 KB
testcase_26 AC 28 ms
4,380 KB
testcase_27 AC 15 ms
4,376 KB
testcase_28 AC 46 ms
4,380 KB
testcase_29 AC 158 ms
4,376 KB
testcase_30 AC 27 ms
4,376 KB
testcase_31 AC 6 ms
4,376 KB
testcase_32 AC 1 ms
4,380 KB
testcase_33 AC 3 ms
4,380 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

#ifdef _RUTHEN
#include <debug.hpp>
#else
#define show(...) true
#endif

using ll = long long;
#define rep(i, n) for (int i = 0; i < (n); i++)
template <class T> using V = vector<T>;

#line 2 "prime/fast-factorize.hpp"

#line 2 "inner/inner_math.hpp"

namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T> T gcd(T a, T b) {
    while (b) swap(a %= b, b);
    return a;
}

template <typename T> T inv(T a, T p) {
    T b = p, x = 1, y = 0;
    while (a) {
        T q = b / a;
        swap(a, b %= a);
        swap(x, y -= q * x);
    }
    assert(b == 1);
    return y < 0 ? y + p : y;
}

template <typename T, typename U> T modpow(T a, U n, T p) {
    T ret = 1 % p;
    for (; n; n >>= 1, a = U(a) * a % p)
        if (n & 1) ret = U(ret) * a % p;
    return ret;
}

}  // namespace inner
#line 2 "misc/rng.hpp"

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
    static u64 _x = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
    _x ^= _x << 7;
    return _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
    assert(l <= r);
    return l + rng() % (r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
    assert(l < r);
    return l + rng() % (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);
    return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }

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 "modint/arbitrary-prime-modint.hpp"

struct ArbitraryLazyMontgomeryModInt {
    using mint = ArbitraryLazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static u32 mod;
    static u32 r;
    static u32 n2;

    static u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u32 m) {
        assert(m < (1 << 30));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u64(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u32 a;

    ArbitraryLazyMontgomeryModInt() : a(0) {}
    ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){};

    static u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; }

    mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u64(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() - mint(*this); }

    mint pow(u64 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) {
        int64_t t;
        is >> t;
        b = ArbitraryLazyMontgomeryModInt(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;
#line 2 "modint/modint-montgomery64.hpp"

struct montgomery64 {
    using mint = montgomery64;
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;
    static u64 n2;

    static u64 get_r() {
        u64 ret = mod;
        for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u64 m) {
        assert(m < (1LL << 62));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u64 a;

    montgomery64() : a(0) {}
    montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

    static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; }

    mint &operator+=(const mint &b) {
        if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i64(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u128(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() - mint(*this); }

    mint pow(u128 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) {
        int64_t t;
        is >> t;
        b = montgomery64(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u64 get() const {
        u64 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
#line 7 "prime/fast-factorize.hpp"

namespace fast_factorize {
using u64 = uint64_t;

template <typename mint> bool miller_rabin(u64 n, vector<u64> as) {
    if (mint::get_mod() != n) mint::set_mod(n);
    u64 d = n - 1;
    while (~d & 1) d >>= 1;
    mint e{1}, rev{int64_t(n - 1)};
    for (u64 a : as) {
        if (n <= a) break;
        u64 t = d;
        mint y = mint(a).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(u64 n) {
    if (~n & 1) return n == 2;
    if (n <= 1) return false;
    if (n < (1LL << 30))
        return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
    else
        return miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

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 = inner::gcd<T>(q.get(), n);
            }
        }
        if (g == n) do
                g = inner::gcd<T>((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) {
    if (n <= 1) return {};
    u64 p;
    if (n <= (1LL << 30))
        p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
    else
        p = pollard_rho<montgomery64, uint64_t>(n);
    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;
        }
        for (int j = v[i].second;; --j) {
            rc(rc, i + 1, x);
            if (j == 0) break;
            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;
using fast_factorize::is_prime;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */

void solve() {
    int N;
    cin >> N;
    V<ll> A(N);
    rep(i, N) cin >> A[i];
    map<ll, int> mp;
    rep(i, N) {
        auto p = factorize(A[i]);
        for (auto &pi : p) mp[pi] ^= 1;
    }
    int ans = 0;
    for (auto a : mp) ans += a.second;
    cout << (ans == 0 ? "Yes" : "No") << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int tt;
    cin >> tt;
    while (tt--) solve();
    return 0;
}
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