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>
int n, a[105], m;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) {
    int s1 = 0, s2 = 0, s3 = 0;
    m = a[i];
    for (int j = 2; j * j <= m; j++) {
      if (m % j == 0) {
        if (s1 == 0)
          s1 = j;
        else
          s2 = j;
        m /= j;
      }
      if (s2 != 0 && m != 1) {
        s3 = a[i] / (s1 * s2);
        if (s2 == s3) s3 = 0;
        break;
      }
    }
    if (s1 * s2 * s3 != 0)
      printf("YES\n%d %d %d", s1, s2, s3);
    else
      printf("NO");
    if (i != n) printf("\n");
  }
  scanf("\n");
}