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;
  while (t--) {
    int n, a, b, c, co = 0, te = 0;
    cin >> n;
    int x[3];
    for (int j = 2; j <= sqrt(n); j++) {
      if (n % j == 0) {
        x[co++] = j;
        n /= j;
        te++;
        if (te == 2) break;
      }
    }
    if (te == 2 && n != 1 && n != x[0] && n != x[1]) {
      cout << "YES" << endl;
      cout << x[0] << " " << x[1] << " " << n << endl;
    } else
      cout << "NO" << endl;
  }
}