//g++ 1.cpp -std=c++14 -O2 -I .
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;

using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vld = vector<ld>;
using vvld = vector<vld>;

#define fi first
#define se second
#define pb push_back
#define pq_big(T) priority_queue<T,vector<T>,less<T>>
#define pq_small(T) priority_queue<T,vector<T>,greater<T>>
#define all(a) a.begin(),a.end()
#define rep(i,start,end) for(ll i=start;i<(ll)(end);i++)
#define per(i,start,end) for(ll i=start;i>=(ll)(end);i--)

#include <cassert>
#include <cmath>
#include <initializer_list>
#include <random>
#include <iostream>
#include <algorithm>

std::mt19937_64 mt{std::random_device{}()};
long long rnd(long long n) { return std::uniform_int_distribution<long long>(0, n-1)(mt); }

bool is_prime(long long x){
  using u128=__uint128_t;
  
  if(x==2||x==3||x==5||x==7)return true;
  if(x%2==0||x%3==0||x%5==0||x%7==0)return false;
  if(x<121){
    return x>1;
  }

  long long d = (x-1) >> __builtin_ctzll(x-1);
  long long one=1,minus_one=x-1;

  auto pow = [](long long x,long long n,long long mod){
    u128 res;
    x%=mod;
    if(n==0){
      res=1;return res;
    }
    res=1;
    u128 now=x;
    for(;n;n>>=1,now=(now*now)%mod){
      if(n&1){
        res=res*now%mod;
      }
    }
    return res;
  };

  auto ok = [&](long long a){
    auto y=pow(a,d,x);
    long long t=d;

    while(y!=one&&y!=minus_one&&t!=x-1){
      y=y*y%x;
      t<<=1;
    }

    if(y!=minus_one&&t%2==0)return false;
    return true;
  };

  if(x<(1ull<<32)){
    for(long long a:{2,7,61}){
      if(!ok(a))return false;
    }
  }
  else{
    for(long long a:{2,325,9375,28178,450775,9780504,1795265022}){
      if(x<=a)return true;
      if(!ok(a))return false;
    }
  }

  return true;
}

long long GCD(long long a,long long b){
  if(b == 0){
    return a;
  }
  else{
    return GCD(b,(a%b));
  }
}

long long rho(long long n,long long c){
  using u128=__uint128_t;

  assert(n>1);
  long long cc=c;

  auto f = [&](long long x){
    long long res;
    res=(((u128)x)*x+cc)%n;
    return res;
  };

  long long x=1,y=2,z=1,q=1;
  long long g=1;

  long long m= 1LL<<((64-__builtin_ctzll(n))/5);

  for(long long r=1;g==1;r<<=1){
    x=y;
    for(int i=0;i<r;i++){
      y=f(y);
    }
    for(long long k=0;k<r&&g==1;k+=m){
      z=y;
      for(long long i=0;i<std::min(m,r-k);i++){
        y=f(y);
        long long w=(x-y)%n;
        if(w<0)w+=n;
        q=((u128)q*w)%n;
      }
      g=GCD(q,n);
    }
  }

  if(g==n){
    do{
      z=f(z);
      long long w=(x-z)%n;
      if(w<0)w+=n;
      g=GCD(w,n);
    }while(g==1);
  }

  return g;
}

long long prime_factor(long long n){
  assert(n>1);
  if(is_prime(n)) return n;

  for(int i=0;i<100;i++){
    long long m=rho(n,rnd(n));
    if(is_prime(m))return m;
    n=m;
  }
  std::cerr<<"failed\n";
  assert(false);
  return -1;
}

std::vector<std::pair<long long,int>> factor(long long n){
  static std::vector<std::pair<long long,int>> res;
  res.clear();

  for(long long i=2;i<=100&&i*i<=n;++i){
    if(n%i==0){
      int cnt=0;
      do{
        cnt++;
        n/=i;
      }while(n%i==0);
      res.emplace_back(i,cnt);
    }
  }

  while(n>1){
    long long p=prime_factor(n);
    int cnt=0;
    do{
      cnt++;
      n/=p;
    }while(n%p==0);
    res.emplace_back(p,cnt);
  }

  std::sort(res.begin(),res.end());
  return res;
}

void solve(){
  ll x;
  cin>>x;

  vi count(50,0);

  auto init=move(factor(x));
  int divisor=1;
  for(auto [value,cnt]:init){
    if(value<50){
      divisor*=(cnt+1);
      count[value]=cnt;
    }
  }

  rep(i,2,40){
    auto check=move(factor(i));
    int div=1;
    for(auto [value,cnt]:check){
      count[value]+=cnt;
    }

    rep(j,0,50){
      div*=(count[j]+1);
    }

    if(div==divisor*2){
      cout<<i*x<<"\n";
      return;
    }

    for(auto [value,cnt]:check){
      count[value]-=cnt;
    }
  }
}

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int t;
  cin>>t;

  while(t--){
    solve();
  }
}