#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("inline")
#include<bits/stdc++.h>
using namespace std;
template<class T> struct cLtraits_identity{
  using type = T;
}
;
template<class T> using cLtraits_try_make_signed =
  typename conditional<
    is_integral<T>::value,
    make_signed<T>,
    cLtraits_identity<T>
    >::type;
template <class S, class T> struct cLtraits_common_type{
  using tS = typename cLtraits_try_make_signed<S>::type;
  using tT = typename cLtraits_try_make_signed<T>::type;
  using type = typename common_type<tS,tT>::type;
}
;
void*wmem;
char memarr[96000000];
template<class S, class T> inline auto min_L(S a, T b)
-> typename cLtraits_common_type<S,T>::type{
  return (typename cLtraits_common_type<S,T>::type) a <= (typename cLtraits_common_type<S,T>::type) b ? a : b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
template<class T> inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){
  walloc1d(arr, x2-x1, mem);
  (*arr) -= x1;
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void rd(long long &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline int rd_int(void){
  int x;
  rd(x);
  return x;
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
inline void wt_L(long long x){
  int s=0;
  int m=0;
  char f[20];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
int Prime_L(int N, int res[], void *mem=wmem){
  int i;
  int a;
  int b;
  int sz = 1;
  const int r = 23000;
  bool*isprime;
  int*sf;
  int ss = 1;
  walloc1d(&isprime, r, &mem);
  walloc1d(&sf, r, &mem);
  N /= 2;
  res[0] = 2;
  b =min_L(r, N);
  for(i=(1);i<(b);i++){
    isprime[i] = 1;
  }
  for(i=(1);i<(b);i++){
    if(isprime[i]){
      res[sz++] = 2*i+1;
      sf[ss] = 2*i*(i+1);
      if(sf[ss] < N){
        while(sf[ss] < r){
          isprime[sf[ss]] = 0;
          sf[ss] += res[ss];
        }
        ss++;
      }
    }
  }
  for(a=r; a<N; a+=r){
    b =min_L(a + r, N);
    isprime -= r;
    for(i=(a);i<(b);i++){
      isprime[i] = 1;
    }
    for(i=(1);i<(ss);i++){
      while(sf[i] < b){
        isprime[sf[i]] = 0;
        sf[i] += res[i];
      }
    }
    for(i=(a);i<(b);i++){
      if(isprime[i]){
        res[sz++] = 2*i+1;
      }
    }
  }
  return sz;
}
int ps;
int p[100];
long long f[100];
long long mf[100][100];
int main(){
  int FmcKpFmN, i;
  wmem = memarr;
  ps =Prime_L(100, p);
  for(i=(2);i<(100);i++){
    int k;
    int j = i;
    for(k=(0);k<(ps);k++){
      while(j%p[k]==0){
        mf[i][k]++;
        j/=p[k];
      }
    }
  }
  int xr20shxY = rd_int();
  for(FmcKpFmN=(0);FmcKpFmN<(xr20shxY);FmcKpFmN++){
    long long N;
    rd(N);
    long long k;
    long long t1;
    long long t2;
    for(i=(0);i<(ps);i++){
      k = N;
      f[i] = 0;
      while(k % p[i] == 0){
        k /= p[i];
        f[i]++;
      }
    }
    int hCmBdyQB;
    remove_reference<decltype(f[hCmBdyQB]+1)>::type V9aVTaxx;
    int APIVbQlN = 0;
    if((0) > ((ps)-1)){
      V9aVTaxx = 1;
    }
    else{
      for(hCmBdyQB = 0; hCmBdyQB <= (ps)-1; hCmBdyQB++){
        if(APIVbQlN == 0){
          V9aVTaxx = f[hCmBdyQB]+1;
          APIVbQlN = 1;
          continue;
        }
        V9aVTaxx *= f[hCmBdyQB]+1;
      }
      if(APIVbQlN==0){
        V9aVTaxx = 1;
      }
    }
    t1 =V9aVTaxx;
    for(k=(2);k<(100);k++){
      for(i=(0);i<(ps);i++){
        f[i] += mf[k][i];
      }
      int BUotOFBp;
      remove_reference<decltype(f[BUotOFBp]+1)>::type Q5rsz4fz;
      int GgkpftXM = 0;
      if((0) > ((ps)-1)){
        Q5rsz4fz = 1;
      }
      else{
        for(BUotOFBp = 0; BUotOFBp <= (ps)-1; BUotOFBp++){
          if(GgkpftXM == 0){
            Q5rsz4fz = f[BUotOFBp]+1;
            GgkpftXM = 1;
            continue;
          }
          Q5rsz4fz *= f[BUotOFBp]+1;
        }
        if(GgkpftXM==0){
          Q5rsz4fz = 1;
        }
      }
      t2 =Q5rsz4fz;
      if(t2 == t1 * 2){
        wt_L(N * k);
        wt_L('\n');
        break;
      }
      for(i=(0);i<(ps);i++){
        f[i] -= mf[k][i];
      }
    }
  }
  return 0;
}
// cLay version 20210717-1 [beta]

// --- original code ---
// int ps, p[100];
// ll f[100], mf[100][100];
// {
//   ps = Prime(100, p);
//   rep(i,2,100){
//     int j = i;
//     rep(k,ps) while(j%p[k]==0) mf[i][k]++, j/=p[k];
//   }
//   REP(rd_int()){
//     ll @N, k, t1, t2;
//     rep(i,ps){
//       k = N;
//       f[i] = 0;
//       while(k % p[i] == 0) k /= p[i], f[i]++;
//     }
//     t1 = mul[i,0,ps](f[i]+1);
//     rep(k,2,100){
//       rep(i,ps) f[i] += mf[k][i];
//       t2 = mul[i,0,ps](f[i]+1);
//       if(t2 == t1 * 2) wt(N * k), break;
//       rep(i,ps) f[i] -= mf[k][i];
//     }
//   }
// }