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() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, cp = 0;
    cin >> n;
    vector<long long int> v1;
    long long int i;
    for (i = 2; i <= sqrt(n); i++) {
      if (n % i == 0 && n / i != i) {
        v1.push_back(i);
        cp++;
        n /= i;
        break;
      }
    }
    if (!cp)
      cout << "NO" << endl;
    else {
      for (long long int j = sqrt(n); j > i; j--) {
        if (n % j == 0 && n / j != j) {
          v1.push_back(j);
          v1.push_back(n / j);
          break;
        }
      }
      if (v1.size() == 3) {
        cout << "YES" << endl;
        cout << v1[0] << " " << v1[1] << " " << v1[2] << endl;
      } else
        cout << "NO" << endl;
    }
  }
  return 0;
}