結果

問題 No.2074 Product is Square ?
ユーザー dn6049949dn6049949
提出日時 2022-09-16 22:00:58
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,141 bytes
コンパイル時間 260 ms
コンパイル使用メモリ 86,776 KB
実行使用メモリ 82,512 KB
最終ジャッジ日時 2023-08-23 15:31:12
合計ジャッジ時間 32,127 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ
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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 98 ms
71,920 KB
testcase_01 AC 736 ms
80,180 KB
testcase_02 AC 716 ms
79,800 KB
testcase_03 AC 716 ms
80,048 KB
testcase_04 AC 711 ms
80,068 KB
testcase_05 AC 755 ms
79,968 KB
testcase_06 AC 718 ms
79,748 KB
testcase_07 AC 722 ms
80,016 KB
testcase_08 AC 684 ms
80,052 KB
testcase_09 AC 666 ms
79,352 KB
testcase_10 AC 668 ms
79,764 KB
testcase_11 AC 348 ms
80,512 KB
testcase_12 AC 802 ms
81,176 KB
testcase_13 TLE -
testcase_14 AC 529 ms
80,640 KB
testcase_15 AC 336 ms
79,708 KB
testcase_16 AC 801 ms
81,668 KB
testcase_17 TLE -
testcase_18 AC 569 ms
80,228 KB
testcase_19 AC 347 ms
80,564 KB
testcase_20 AC 791 ms
81,740 KB
testcase_21 TLE -
testcase_22 AC 531 ms
81,492 KB
testcase_23 AC 341 ms
79,584 KB
testcase_24 AC 828 ms
81,260 KB
testcase_25 TLE -
testcase_26 AC 553 ms
80,804 KB
testcase_27 AC 333 ms
79,964 KB
testcase_28 AC 834 ms
82,512 KB
testcase_29 TLE -
testcase_30 AC 545 ms
80,744 KB
testcase_31 AC 108 ms
77,032 KB
testcase_32 AC 95 ms
72,216 KB
testcase_33 AC 121 ms
77,464 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 # 

from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def IR(n):
    return [I() for _ in range(n)]
def LIR(n):
    return [LI() for _ in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007


def gcd(a, b):
    while a:
        a, b = b%a, a
    return b


def is_prime(n):
    if n == 2:
        return 1
    if n == 1 or n%2 == 0:
        return 0

    m = n - 1
    lsb = m & -m
    s = lsb.bit_length()-1
    d = m // lsb
    if n < 4759123141:
        test_numbers = [2, 7, 61]
    elif n < 341550071728321:
        test_numbers = [2, 3, 5, 7, 11, 13, 17]
    elif n < 3825123056546413051:
        test_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23]
    else:
        test_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]

    for a in test_numbers:
        if a == n:
            continue
        x = pow(a,d,n)
        r = 0
        if x == 1:
            continue
        while x != m:
            x = pow(x,2,n)
            if x == 1 or r == s:
                return 0
            r += 1
    return 1


def find_prime_factor(n):
    m = 2*int(2**(((n.bit_length()-1)>>2)/2))

    for c in range(1,n):
        f = lambda a: (pow(a,2,n)+c)%n
        y = 0
        g = q = r = 1
        while g == 1:
            x = y
            for _ in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for _ in range(min(m, r-k)):
                    y = f(y)
                    q = q*abs(x-y)%n
                g = gcd(q,n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            y = ys
            while g == 1:
                y = f(y)
                g = gcd(abs(x-y),n)
        if g == n:
            continue
        if is_prime(g):
            return g
        elif is_prime(n//g):
            return n//g
        else:
            n = g


def factorize(n):
    res = {}
    for p in range(2,1000):
        if p*p > n:
            break
        if n%p:
            continue
        s = 0
        while n%p == 0:
            n //= p
            s += 1
        res[p] = s

    while not is_prime(n) and n > 1:
        p = find_prime_factor(n)
        s = 0
        while n%p == 0:
            n //= p
            s += 1
        res[p] = s
    if n > 1:
        res[n] = 1
    return res


def main():
    n = I()
    a = LI()
    a.sort()
    s = defaultdict(lambda : 0)
    for i in a[:-1]:
        f = factorize(i)
        for i,j in f.items():
            s[i] ^= j&1
    a = a[-1]
    for i,j in s.items():
        if j:
            if a%i:
                print("No")
                return
            a //= i
    l = 0
    r = a+1
    while l+1 < r:
        m = (l+r) >> 1
        if m**2 <= a:
            l = m
        else:
            r = m

    if l**2 == a:
        print("Yes")
    else:
        print("No")
    return


if __name__ == "__main__":
    for _ in range(I()):
        main()
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