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 q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int n;
    cin >> n;
    set<int> used;
    for (int i = 2; i * i <= n; ++i) {
      if (n % i == 0 && !used.count(i)) {
        used.insert(i);
        n /= i;
        break;
      }
    }
    for (int i = 2; i * i <= n; ++i) {
      if (n % i == 0 && !used.count(i)) {
        used.insert(i);
        n /= i;
        break;
      }
    }
    if (int(used.size()) < 2 || used.count(n) || n == 1) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
      used.insert(n);
      for (auto it : used) cout << it << " ";
      cout << endl;
    }
  }
  return 0;
}