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 n;
  cin >> n;
  while (n--) {
    int flag = 0;
    long long int q;
    cin >> q;
    for (long int i = 2; i <= sqrt(q); i++) {
      if (q % i == 0) {
        for (long int j = i + 1; j <= sqrt(q / i); j++) {
          if ((q / i) % j == 0 && j != ((q / i) / j)) {
            flag = 1;
            cout << "YES" << endl;
            cout << i << " " << j << " " << (q / i) / j << endl;
            break;
          }
        }
        if (flag == 1) break;
      }
    }
    if (flag == 0) cout << "NO" << endl;
  }
}