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 solve() {
  long long int n;
  cin >> n;
  long long int ans[3];
  long long int count = 0;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      n = n / i;
      ans[count] = i;
      count++;
    }
    if (count == 3) {
      break;
    }
  }
  if (count == 3 && n > 2) {
    ans[2] = ans[2] * n;
  } else if (count < 3 && n > 2) {
    ans[count] = n;
    count++;
  }
  if (count == 3 && ans[0] != ans[1] && ans[1] != ans[2] && ans[2] != ans[0]) {
    cout << "YES" << endl;
    cout << ans[0] << " " << ans[1] << " " << ans[2] << endl;
  } else
    cout << "NO" << endl;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}