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::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, q;
  cin >> q;
  while (q--) {
    cin >> n;
    vector<int> res;
    for (int i = 2; res.size() < 2 && i * i < n; ++i) {
      if (n % i == 0) {
        res.push_back(i);
        n /= i;
      }
    }
    res.push_back(n);
    if (res.size() != 3) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
      cout << res[0] << " " << res[1] << " " << res[2] << endl;
    }
  }
}