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;
bool isPrime(int n) {
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) return false;
  }
  return true;
}
int main() {
  int tc;
  cin >> tc;
  while (tc--) {
    int n;
    cin >> n;
    if (isPrime(n)) {
      cout << "NO" << endl;
    } else {
      vector<int> factores;
      for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
          if (factores.size() == 0)
            factores.push_back(i);
          else if (i > factores.back())
            factores.push_back(i);
          n /= i;
        }
      }
      if (n > 2) factores.push_back(n);
      if (factores.size() < 3) {
        cout << "NO" << endl;
      } else {
        int f = 1;
        for (int i = 2; i < factores.size(); i++) f = f * factores[i];
        if (f > factores[1]) {
          cout << "YES" << endl;
          cout << factores[0] << " " << factores[1] << " ";
          cout << f << endl;
        } else {
          cout << "NO" << endl;
        }
      }
    }
  }
  return 0;
}