prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
def solve():
    x = int(input())
    for i in range(2, 32):
        if x % i != 0:
            print(x * i)
            return
        a = 1
        b = 1
        X = x
        for p in prime:
            cnt = 0
            while X % p == 0:
                X //= p
                cnt += 1
            b *= cnt + 1
            I = i
            while I % p == 0:
                I //= p
                cnt += 1
            a *= cnt + 1
        if a == 2 * b:
            print(x * i)
            return
            
    
for _ in range(int(input())):
    solve()