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;
set<int> v;
void solve() {
  int n;
  cin >> n;
  int nn = n;
  v.clear();
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) {
      v.insert(i);
      n /= i;
    }
  if (n > 1) v.insert(n);
  if (v.size() <= 2) {
    cout << "NO" << endl;
    return;
  }
  cout << "YES" << endl;
  int s1 = *v.begin();
  v.erase(v.begin());
  int s2 = *v.begin();
  v.erase(v.begin());
  cout << s1 << ' ' << s2 << ' ' << nn / (s1 * s2) << endl;
}
int main() {
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}