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() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, a = 2, b = 1, c = 1, t, cnt = 0;
    cin >> n;
    t = n;
    while (cnt < 2 && n > 1) {
      if (n % a == 0) {
        if (cnt == 0) {
          b = a;
        } else {
          c = a;
        }
        n = n / a;
        cnt++;
        a++;
      } else if (a * a >= n) {
        break;
      } else
        a++;
    }
    if (cnt == 2 && c != t / (b * c) && b != t / (b * c) && t / (b * c) != 1) {
      cout << "YES\n";
      cout << b << " " << c << " " << t / (b * c) << endl;
    } else {
      cout << "NO\n";
    }
  }
}