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 isPrime(int n) {
  if (n <= 1) return 0;
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) return 0;
  return 1;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (isPrime(n))
      cout << "NO\n";
    else {
      int c = 0;
      vector<int> a;
      int prev = 0;
      for (int i = 2; i * i < n; i++) {
        if ((a.size() == 2) && (n != prev)) break;
        if (n % i == 0) {
          if (prev != i) {
            a.push_back(i);
            prev = i;
          }
          n = n / i;
        }
      }
      if (a.size() < 2)
        cout << "NO\n";
      else {
        cout << "YES\n";
        cout << a[0] << " " << a[1] << " " << n << "\n";
      }
    }
  }
}