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--) {
    long long n;
    cin >> n;
    int cnt = 0;
    vector<long long> ans;
    for (long long i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        if (cnt == 0) {
          ans.push_back(i);
          n = n / i;
          cnt++;
        } else {
          ans.push_back(i);
          ans.push_back(n / i);
          break;
        }
      }
    }
    if ((ans.size() == 3) && (ans[0] != ans[1]) && (ans[1] != ans[2]) &&
        (ans[0] != ans[2])) {
      cout << "YES" << endl;
      cout << ans[0] << " " << ans[1] << " " << ans[2] << endl;
    } else
      cout << "NO" << endl;
  }
  return 0;
}