#include <stdio.h>
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 1000000000000000000
vector<long long> p;

vector<long long> get(long long X){
	vector<long long> ret(p.size(),0);
	rep(i,p.size()){
		long long cur = p[i];
		rep(j,100){
			if(X%cur!=0){
				ret[i] = j;
				break;
			}
			cur *= p[i];
		}
	}
	return ret;
}

vector<long long> add(vector<long long> a,vector<long long> b){
	rep(i,a.size()){
		a[i] += b[i];
	}
	return a;
}

long long get(vector<long long> a){
	long long ret = 1LL;
	rep(i,a.size())ret *= a[i]+1;
	return ret;
}

int main(){
	
	
	
	for(long long i=2;true;i++){
		if(p.size()>30)break;
		bool f = true;
		rep(j,p.size()){
			if(i%p[j]==0){
				f = false;
				break;
			}
		}
		if(f)p.push_back(i);
	}
	
	int _t;
	cin>>_t;
	
	rep(_,_t){
		long long X;
		scanf("%lld",&X);
		auto temp = get(X);
		int Y = get(temp);
		
		for(long long i=2;true;i++){
			auto t2 = get(i);
			if(Y*2==get(add(temp,t2))){
				cout<<X*i<<endl;
				break;
			}
		}
		
		
	}
	
	return 0;
}