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 factor(int y, int z) {
  for (int i = z + 1; i * i <= y; i++) {
    if (y % i == 0) return i;
  }
  return 0;
}
int main() {
  int t;
  cin >> t;
  while (t > 0) {
    int n;
    cin >> n;
    int x = factor(n, 1);
    if (x >= 2) {
      int m = factor(n / x, x);
      if (m >= 2 && m != x) {
        int z = n / (x * m);
        if (z != x && z != m && z >= 2) {
          cout << "yes" << endl;
          cout << x << " " << m << " " << z << endl;
        } else
          cout << "no" << endl;
      } else
        cout << "no" << endl;
    } else
      cout << "no" << endl;
    t--;
  }
}