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;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, arr[10];
    cin >> n;
    int cnt = 0;
    for (int i = 2; i < sqrt(n); i++) {
      if (n % i == 0 && ((n / i) != i)) {
        arr[0] = i;
        n = n / i;
        cnt = 5;
        break;
      }
    }
    if (cnt != 5)
      cout << "NO" << endl;
    else {
      for (int i = 2; i < sqrt(n); i++) {
        if (n % i == 0 && ((n / i) != i) && (arr[0] != i) &&
            (arr[0] != n / i)) {
          arr[1] = i;
          arr[2] = n / i;
          cnt = 10;
          break;
        }
      }
      if (cnt != 10)
        cout << "NO" << endl;
      else {
        cout << "YES" << endl;
        cout << arr[0] << " " << arr[1] << " " << arr[2] << endl;
      }
    }
  }
}