#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[8]={-1,0,1,0,1,1,-1,-1};
const ll dx[8]={0,-1,0,1,1,-1,1,-1};
template <typename T> inline bool chmax(T &a, T b) {
  return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
  return ((a > b) ? (a = b, true) : (false));
}
vl prime={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47};
ll power(ll n,ll k){
  ll res=1;
  rep(i,k)res*=n;
  return res;
}
ll ans;
ll cnt;
void dfs(map<ll,ll> mp, ll now){
  ll div=1;
  for(auto p:prime)div*=mp[p]+1;
  if(div==cnt*2){
    chmin(ans,now);return;
  }
  if(div>cnt*2)return;
  for(auto p:prime){
    now*=p;mp[p]++;
    dfs(mp,now);
    now/=p;mp[p]--;
  }
}
void solve(ll n){
  ans=INF;
  map<ll,ll> mp;
  ll k=n;
  for(auto p:prime){
    while(k%p==0){
      k/=p;mp[p]++;
    }
  }
  cnt=1;
  for(auto p:prime){
    cnt*=mp[p]+1;
  }
  dfs(mp,1);
  cout << ans*n <<endl;
}
int main(){
  ll t;cin >> t;
  while(t--){
    ll x;cin >> x;
    solve(x);
  }
}