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;
const long long MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0);
  ;
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int curr = n;
    vector<int> ans;
    bool ok = true;
    while (ans.size() < 2 && ok) {
      int currMax = (int)sqrt(curr) + 1;
      int i = 2;
      if (ans.size()) {
        i = ans[ans.size() - 1] + 1;
      }
      while (i < currMax) {
        if (curr % i == 0) {
          ans.push_back(i);
          curr /= i;
          break;
        }
        i++;
      }
      if (i >= currMax) {
        ok = false;
      }
    }
    if (ans.size() == 2 && ans[1] != n / ans[0] / ans[1]) {
      cout << "YES\n"
           << ans[0] << " " << ans[1] << " " << n / ans[0] / ans[1] << "\n";
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}