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() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  srand(time(NULL));
  ;
  int q;
  cin >> q;
  while (q--) {
    long long n;
    cin >> n;
    vector<long long> ans;
    for (long long i = 2; i <= sqrt(n); i++) {
      if (n % i == 0) {
        ans.push_back(i);
        n = n / i;
      }
      if (n == 1) break;
      if (ans.size() == 2) break;
    }
    if (ans.size() < 2 || n == ans[0] || n == 1 || n == ans[1])
      cout << "NO" << endl;
    else {
      cout << "YES" << endl << ans[0] << " " << ans[1] << " " << n << endl;
    }
  }
}