def primes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

pr = primes(200)
t = int(input())
for _ in range(t):
    x = int(input())
    ans = 10 ** 18
    l = [(0, 100000)]
    for p in pr:
        cnt = 1
        t = x
        while t % p == 0:
            t //= p
            cnt += 1
        if l[-1][1] > cnt:
            res = x
            l.append((p, cnt))
            for i in range(len(l) - 1, 0, -1):
                if l[i - 1][1] >= cnt * 2:
                    res *= pow(l[i][0], cnt * 2 - l[i][1])
                    break
                else:
                    res *= pow(l[i][0], l[i - 1][1] - l[i][1])
            ans = min(ans, res)
        if x % p > 0:
            break
    print(ans)