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--) {
    long long n;
    cin >> n;
    long long temp = n;
    vector<long long> v;
    for (long long i = 2; i <= sqrt(n); i++) {
      while (n % i == 0) {
        v.push_back(i);
        n /= i;
      }
    }
    if (n != 1) {
      v.push_back(n);
    }
    if (v.size() < 3) {
      cout << "No" << endl;
      continue;
    }
    long long fi = v[0];
    long long se = v[1];
    if (se == fi) {
      se = se * v[2];
    }
    long long th = temp / (fi * se);
    if (th != fi && th != se && th != 1) {
      cout << "Yes" << endl;
      cout << fi << " " << se << " " << th << endl;
    } else
      cout << "No" << endl;
  }
}