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 int ma1 = 3e5 + 5;
string no = "NO", yes = "YES";
const unsigned int MAX1 = 1000000007;
void f(int n) {
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      int d = n / i;
      for (int j = i + 1; j < sqrt(d); j++) {
        if (d % j == 0) {
          cout << yes << endl;
          cout << i << " " << j << " " << d / j << endl;
          return;
        }
      }
    }
  }
  cout << no << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    f(n);
  }
}