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 t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> v;
    int m = n;
    for (int i = 2; i <= sqrt(m); i++) {
      if (m % i == 0) {
        v.push_back(i);
        m /= i;
        break;
      }
    }
    for (int i = 2; i <= sqrt(m); i++) {
      if (m % i == 0 && v[0] != i) {
        v.push_back(i);
        m /= i;
        break;
      }
    }
    if (v.size() < 2 || n == 1 || v[0] == m || v[1] == m)
      cout << "NO" << endl;
    else {
      int x = v[0] * v[1];
      int y = n / x;
      cout << "YES" << endl;
      cout << v[0] << " " << v[1] << " " << y << endl;
    }
  }
  return 0;
}