#include <bits/stdc++.h>
#include <atcoder/all>
typedef long long int ll;
typedef long long int ull;
#define MP make_pair
using namespace std;
using namespace atcoder;
typedef pair<ll, ll> P;
const ll MOD = 998244353;
// const ll MOD = 1000000007;
using mint = modint998244353;
// using mint = modint1000000007;
const double pi = 3.1415926536;
const int MAX = 2000003;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
// 二項係数計算
long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
ll gcd(ll x, ll y) {
   if (y == 0) return x;
   else if (y > x) {
       return gcd (y, x); 
   }
   else return gcd(x % y, y);
}
ll lcm (ll x, ll y) {
   return x / gcd(x, y) * y;
}
ll my_sqrt(ll x) {
    ll m = 0;
    ll M = 3000000001;
    while (M - m > 1) {
        ll now = (M + m) / 2;
        if (now * now <= x) {
            m = now;
        }
        else {
            M = now;
        }
    }
    return m;
}
ll keta(ll n) {
    ll ret = 0;
    while (n) {
        n /= 10;
        ret++;
    }
    return ret;
}
ll ceil(ll n, ll m) {
    // n > 0, m > 0
    ll ret = n / m;
    if (n % m) ret++;
    return ret;
}
ll pow_ll(ll x, ll n) {
    if (n == 0) return 1;
    if (n % 2) {
        return pow_ll(x, n - 1) * x;
    }
    else {
        ll tmp = pow_ll(x, n / 2);
        return tmp * tmp;
    }
}

int main() {
    ll prime[11] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
    int t;
    cin >> t;
    for (int t_i = 1; t_i <= t; t_i++) {
        ll x;
        cin >> x;
        ll X = x;
        ll num[11];
        for (int i = 0; i < 11; i++) num[i] = 0;
        for (int i = 0; i < 11; i++) {
            while (x % prime[i] == 0) {
                x /= prime[i];
                num[i]++;
            }
        }
        for (ll i = 2; i <= 31; i++) {
            ll I = i;
            ll tmp[11];
            for (int j = 0; j < 11; j++) tmp[j] = 0;
            for (int j = 0; j < 11; j++) {
                while (I % prime[j] == 0) {
                    I /= prime[j];
                    tmp[j]++;
                }
            }
            ll p = 1;
            ll q = 1;
            for (int j = 0; j < 11; j++) p*=(num[j] + 1);
            for (int j = 0; j < 11; j++) q*=(num[j] + tmp[j] + 1);
            // cout << i << ' ' << p << ' ' <<  q << endl;
            if (p * 2 == q) {
                cout << i * X << endl;
                break;
            }
        }
    }
    return 0;
}