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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t;
  cin >> t;
  while (t--) {
    long long n, f = 0;
    cin >> n;
    long long i = 2;
    while (i * i < n) {
      if (n % i == 0) {
        f = 1;
        break;
      }
      i++;
    }
    n = n / i;
    if (n > i && f) {
      f = 0;
      long long j = i + 1;
      while (j * j < n) {
        if (n % j == 0) {
          f = 1;
          break;
        }
        j++;
      }
      n /= j;
      if (f && n > j) cout << "YES\n" << i << " " << j << " " << n << "\n";
    }
    if (f == 0) cout << "NO\n";
  }
  return 0;
}