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, i;
  long n, d, arr[2];
  cin >> t;
  while (t--) {
    cin >> n;
    i = 0;
    for (d = 2; d * d < n && i < 2; d++) {
      if (n % d == 0) {
        arr[i++] = d;
        n /= d;
      }
    }
    if (i == 2)
      cout << "YES\n" << arr[0] << ' ' << arr[1] << ' ' << n << '\n';
    else
      cout << "NO\n";
  }
  return 0;
}