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 Doaa() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int main() {
  Doaa();
  int n, t, num1 = 0, count = 0;
  cin >> t;
  while (t--) {
    count = 0;
    cin >> n;
    int x = n;
    bool f = true;
    for (int i = 2; i <= sqrt(n); i++) {
      if (n % i == 0) {
        if (count == 0) {
          num1 = i;
          n = n / i;
        }
        count++;
      }
      if (count == 2) {
        x = i;
        if (i * i == n)
          f = false;
        else {
          if (n / i == num1)
            f = false;
          else
            f = true;
          break;
        }
      }
    }
    if (count == 2 && f)
      cout << "YES" << endl << num1 << " " << x << " " << n / x << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}