#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REPR(i, n) for (int i = n - 1; i >= 0; --i)
#define FOR(i, m, n) for (int i = m; i < n; ++i)
#define FORR(i, m, n) for (int i = m; i >= n; --i)
#define ALL(v) (v).begin(),(v).end()
#define ALLR(v) (v).rbegin(),(v).rend()
#define fi first
#define se second
#define PB push_back
#define EB emplace_back
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T>void debug(const T &v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j]<<" \n"[j==w-1];}};
template<typename T>void debug(const T &v,ll n){for(ll i=0;i<n;i++)cout<<v[i]<<" \n"[i==n-1];};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
const ll INF=1LL<<60;
const int inf=(1<<30)-1;
// const int mod=1e9+7;
const int mod=998244353;
int dx[8]={1,0,-1,0,-1,-1,1,1};
int dy[8]={0,1,0,-1,-1,1,-1,1};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int T;cin >> T;
    while(T--){
        ll x;cin >> x;
        ll num=x;
        map<ll,ll> mp;
        for(ll i=2;i<50;i++){
            int cnt=0;
            while(num%i==0){
                num/=i;
                cnt++;
                mp[i]=cnt;
            }
        }
        if(num!=1) mp[num]=1;
        FOR(i,2,50){
            ll u=1,v=1;
            int nm=i;
            for(ll i=2;i*i<=nm;i++){
                int cnt=0;
                while(nm%i==0){
                    nm/=i;
                    cnt++;
                }
                u*=mp[i]+1;
                v*=cnt+mp[i]+1;
            }
            if(nm!=1){
                u*=mp[nm]+1;
                v*=mp[nm]+2;
            }
            if(u*2==v){
                cout << x*i << endl;
                break;
            }
        }
    }
}