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 parr(int arr[], int n, string name) {
  int i;
  for (i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "\n";
}
template <typename T>
void p(T x, string name = " ") {
  cout << name << " : " << x << "\n";
}
void fn(int n) {
  int a, b, c;
  int i, j, temp;
  bool found = false;
  for (i = 2; i * i <= n; i++) {
    temp = n;
    if (temp % i == 0) {
      a = i;
      temp = temp / a;
      for (j = 2; j * j <= temp; j++) {
        if (j != a && temp % j == 0) {
          b = j;
          c = n / (a * b);
          if (c != a && c != b && c != 1) {
            cout << "YES\n";
            cout << a << " " << b << " " << c;
            found = true;
            break;
          }
        }
      }
      if (found) break;
    }
  }
  if (!found) cout << "NO";
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    fn(n);
    cout << "\n";
  }
}