Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using namespace std;
void solve() {
  int n;
  cin >> n;
  int arr[3];
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      arr[0] = i;
      n /= i;
      break;
    }
  }
  bool good1 = false;
  for (int j = 2; j <= sqrt(n); j++) {
    if (n % j == 0) {
      if (j != n && j != arr[0]) {
        arr[1] = j;
        n /= j;
        good1 = true;
        break;
      }
    }
  }
  if (n != arr[0] && n != arr[1] && n != 1 && good1)
    cout << "YES\n" << arr[0] << " " << arr[1] << " " << n << "\n";
  else
    cout << "NO\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout << fixed;
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}