#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;
using ll = long long;

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

    int t;
    cin>>t;
    const int mx = 3e5;
    vector<int> cnt(mx+1,0);
    vector<int> use;
    for(int i = 2;i<=mx;i++){
        if(cnt[i]) continue;
        use.push_back(i);
        for(int j = i;j<=mx;j+=i) cnt[j] = 1;
    }
    while(t--){
        ll a;
        cin>>a;
        ll ans = a * 100;
        for(auto&e:use){
            if(a*e>ans) break;
            int cnt = 0;
            ll b = a;
            while(b%e==0){
                b /= e;
                cnt++;
            }
            int m = cnt + 1;
            int want = 2 * m - 1;
            ll now = a;
            for(int i = 0;i<want-cnt;i++) {
                now *= e;
                if(now>ans) break;
            }
            ans = min(ans,now);
        }
        cout<<ans<<endl;
    }
}