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;
void solve() {
  set<int> s;
  int n, i, a, l, p = 1, pr = 1;
  cin >> n;
  l = n;
  for (i = 2; i * i <= l; i++) {
    if (n % i == 0 && p < 3) {
      s.insert(i);
      n = n / i;
      if (p == 2 && n != 1) {
        s.insert(n);
      }
      p++;
    }
  }
  for (set<int>::iterator i = s.begin(); i != s.end(); i++) {
    pr = pr * (*i);
  }
  if (s.size() > 2 && pr == l) {
    cout << "YES\n";
    for (set<int>::iterator i = s.begin(); i != s.end(); i++) cout << *i << " ";
    cout << "\n";
  } else
    cout << "NO\n";
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}