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() {
  int n, i, cnt = 0, d, ar[3];
  cin >> n;
  for (i = 2; i * i <= n; i++)
    if (n % i == 0) {
      ar[cnt++] = i;
      n /= i;
      if (cnt == 2) break;
    }
  if (cnt == 2) {
    ar[2] = n;
    sort(ar, ar + 3);
    if (ar[0] != ar[1] && ar[1] != ar[2]) {
      cout << "YES\n" << ar[0] << ' ' << ar[1] << ' ' << ar[2] << '\n';
      return;
    }
  }
  cout << "NO\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int T;
  cin >> T;
  while (T--) solve();
  return 0;
}