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;
  cin >> t;
  for (int i = 0; i < t; i++) {
    long long int a, b, c, n;
    cin >> n;
    int e = 0;
    long long int d;
    for (int j = 2; j <= (int)sqrt(n); j++) {
      if (n % j == 0) {
        e = 1;
        d = n / j;
        a = j;
        break;
      }
    }
    if (e == 0)
      cout << "NO\n";
    else {
      for (int j = a + 1; j <= (int)sqrt(d); j++) {
        if (d % j == 0 && j != d / j) {
          e = 2;
          b = j;
          c = d / j;
          break;
        }
      }
      if (e == 2)
        cout << "YES\n" << a << " " << b << " " << c << "\n";
      else
        cout << "NO\n";
    }
  }
}