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--) {
    set<int> s;
    int count = 0;
    int a;
    cin >> a;
    for (int i = 2; i * i <= a; i++) {
      if (a % i == 0) {
        int u = a / i;
        s.insert(i);
        for (int j = i + 1; j * j <= u; j++) {
          if (u % j == 0) {
            s.insert(j);
            if (s.find(u / j) == s.end()) {
              count = 1;
              cout << "YES" << endl;
              cout << i << " " << j << " " << u / j << endl;
            }
            break;
          }
        }
      }
      if (count == 1) {
        break;
      }
    }
    if (count == 0) {
      cout << "NO" << endl;
    }
  }
  return 0;
}