import sys
readline = sys.stdin.readline
from collections import *

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    return arr

T = int(readline())
for _ in range(T):
    X = int(readline())
    L = factorization(X)
    D = defaultdict(int)
    for i, cnt in L:
        D[i] += cnt
    num = 1
    for k, v in D.items():
        num *= v + 1
        
    for i in range(2, 32):
        L = factorization(i)
        num2 = 1
        for j, cnt in L:
            D[j] += cnt
        for k, v in D.items():
            num2 *= v + 1
        if num2 == num * 2:
            print(i * X)
            break
        for j, cnt in L:
            D[j] -= cnt