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())
L = [None] * 32
for i in range(2, 32):
    L[i] = factorization(i)
    
prime = [2,3,5,7,11,13,17,19,23,29,31]
for _ in range(T):
    X = int(readline())
    XX = X
    D = defaultdict(int)
    for p in prime:
        while X % p == 0:
            D[p] += 1
            X //= p
    num = 1
    for k, v in D.items():
        num *= v + 1
        
    for i in range(2, 32):
        for j, cnt in L[i]:
            D[j] += cnt
        num2 = 1
        for k, v in D.items():
            num2 *= v + 1
        if num2 == num * 2:
            print(i * XX)
            break
        for j, cnt in L[i]:
            D[j] -= cnt