import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

import math

def sieve(n):
    ass = []
    is_prime = [True]*(n+1)
    is_prime[0] = False
    is_prime[1] = False

    for i in range(2, int(math.sqrt(n))+1):
        if not is_prime[i]:
            continue
        for j in range(i*2, n+1, i):
            is_prime[j] = False
    for i in range(n+1):
        if is_prime[i]:
            ass.append(i)
    return(ass)

P = sieve(35)

t = int(input())
for _ in range(t):
    x = int(input())
    ans = -1
    cnt1 = [0]*len(P)
    y = x
    for j, p in enumerate(P):
        while y%p == 0:
            cnt1[j] += 1
            y //= p
    c1 = 1
    for c in cnt1:
        c1 *= (c+1)
    for i in range(2, 32):
        cnt2 = [0]*len(P)
        z = i
        for j, p in enumerate(P):
            while z%p == 0:
                cnt2[j] += 1
                z //= p
        c2 = 1
        for j, c in enumerate(cnt2):
            c2 *= (cnt1[j]+c+1)
        if c2%c1 == 0 and c2//c1 == 2:
            ans = i*x
            break
    print(ans)