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