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;
void gao(int n) {
  for (int i = 2; i * i < n; i++) {
    if (n % i == 0) {
      for (int j = i + 1; j * j < n / i; j++) {
        if (n / i % j == 0) {
          cout << "YES" << endl;
          cout << i << ' ' << j << ' ' << n / i / j << endl;
          return;
        }
      }
    }
  }
  cout << "NO" << endl;
  return;
}
int main() {
  int t, n;
  cin >> t;
  for (int tt = 0; tt < t; tt++) {
    cin >> n;
    gao(n);
  }
  return 0;
}