import sys

sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def LS2(): return list(sys.stdin.readline().rstrip())


T = I()
primes = [2,3,5,7,11,13,17,19,23,29,31]
prime_fac = [[0]*11 for _ in range(32)]
for i in range(11):
    p = primes[i]
    for j in range(p,32,p):
        k = j
        count = 0
        while k % p == 0:
            count += 1
            k //= p
        prime_fac[j][i] = count

for _ in range(T):
    N = I()
    index = [0]*11
    for i in range(11):
        M = N
        p = primes[i]
        count = 0
        while M % p == 0:
            count += 1
            M //= p
        index[i] = count
    d = 1
    for i in index:
        d *= i+1

    for i in range(2,32):
        dd = 1
        for j in range(11):
            dd *= index[j]+1+prime_fac[i][j]
        if dd == 2*d:
            print(N*i)
            break