from collections import defaultdict
import math
def sieve_of_eratosthenes(n):
    prime = [True]*(n+1)
    prime[0] = False
    prime[1] = False
    sqrt_n = math.ceil(math.sqrt(n))
    for i in range(2, sqrt_n+1):
        if prime[i]:
            for j in range(2*i, n+1, i):
                prime[j] = False
    return prime

p = sieve_of_eratosthenes(31)
num = []
for i in range(len(p)):
    if p[i]:
        num.append(i)

Y = defaultdict(dict)
for i in range(2,32):
    y = i
    for j in num:
        while y%j==0:
            if j in Y[i]:
                Y[i][j] += 1
            else:
                Y[i][j] = 1
            y //= j

T = int(input())
for i in range(T):
    N = int(input())
    X = N
    s = defaultdict(int)
    for j in range(len(num)):
        while X%num[j]==0:
            s[num[j]] += 1
            X //= num[j]
    cnt = 1
    for key in s.keys():
        cnt *= s[key]+1
    for key in Y.keys():
        cnt2 = cnt
        for key2 in Y[key].keys():
            cnt2 //= s[key2]+1
            cnt2 *= s[key2]+Y[key][key2]+1
        if cnt2==cnt*2:
            print(N*key)
            break