def Prime_Factorization(N):
    if N<0:
        R=[[-1,1]]
    else:
        R=[]

    N=abs(N)

    if N&1==0:
        C=0
        while N&1==0:
            N>>=1
            C+=1
        R.append([2,C])

    if N%3==0:
        C=0
        while N%3==0:
            N//=3
            C+=1
        R.append([3,C])

    k=5
    Flag=0
    while k*k<=N:
        if N%k==0:
            C=0
            while N%k==0:
                C+=1
                N//=k
            R.append([k,C])
        k+=2+2*Flag
        Flag^=1

    if N!=1:
        R.append([N,1])

    return R

def solve(X):
    L=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

    D=defaultdict(int)
    for y in L:
        if X%y!=0:
            break
        else:
            t=0
            x=X
            while x%y==0:
                t+=1
                x//=y
            D[y]=t

    for u in range(2,y):
        alpha=beta=1
        for p,e in S[u]:
            alpha*=1+D[p]
            beta *=1+D[p]+e

        if 2*alpha==beta:
            return u*X

    return y*X
#================================================
import sys
from collections import defaultdict

input=sys.stdin.readline
write=sys.stdout.write

S=[[]]
for a in range(1,101):
    S.append(Prime_Factorization(a))

T=int(input())

Ans=[]
for _ in range(T):
    X=int(input())
    Ans.append(solve(X))

write("\n".join(map(str,Ans)))