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;
  for (int g = 0; g < t; ++g) {
    int n;
    cin >> n;
    vector<int> v;
    for (int i = 2; i <= int(sqrt(n)); ++i) {
      if (n % i == 0) {
        v.push_back(i);
        v.push_back(n / i);
      }
    }
    bool T = false;
    for (int i = 0; i < v.size(); ++i) {
      for (int j = i + 1; j < v.size(); ++j) {
        for (int k = j + 1; k < v.size(); ++k) {
          if (v[i] * v[j] * v[k] == n) {
            cout << "YES" << '\n' << v[i] << ' ' << v[j] << ' ' << v[k] << '\n';
            T = true;
            break;
          }
        }
        if (T) break;
      }
      if (T) break;
    }
    if (!T) cout << "NO" << '\n';
  }
  return 0;
}