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;
const int N = 2e5 + 5, MOD = 1e9 + 7;
int t, n, a, b, c;
int main() {
  cin >> t;
  while (t--) {
    cin >> n;
    for (int i = 2; i * i <= n; ++i)
      if (n % i == 0) {
        a = i;
        break;
      }
    if (a)
      for (int i = 2; i * i <= n / a; ++i)
        if ((n / a) % i == 0 && a != i) {
          b = i;
          break;
        }
    if (a && b && a != b && a != n / (a * b) && b != n / (a * b) &&
        n % (a * b) == 0)
      cout << "YES" << endl << a << " " << b << " " << n / (a * b) << endl;
    else
      puts("NO");
  }
  return 0;
}