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 n, m;
int main() {
  int a, b, c, d, t;
  scanf("%d", &t);
  while (t--) {
    int flag = 0;
    scanf("%d", &n);
    a = 0;
    b = 0;
    for (int i = 2; i < sqrt(n); i++) {
      if (n % i == 0) {
        if (a == 0) {
          a = i;
          n /= i;
        } else {
          b = i;
          n /= i;
          if (a < b && b < n) flag = 1;
          break;
        }
      }
    }
    if (flag)
      printf("YES\n%d %d %d\n", a, b, n);
    else
      printf("NO\n");
  }
  return 0;
}