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 tab[50000];
int main() {
  int t;
  int long long n, a, b, c, maxi;
  scanf("%lld", &t);
  while (t--) {
    int s = 0;
    int long long i = 2, j = 2, sq;
    scanf("%lld", &n);
    sq = sqrt(n);
    while (n != 0 && i <= sq) {
      if (n % i == 0) {
        tab[s] = i;
        s++;
        if (s == 2) break;
        n /= i;
      }
      i++;
    }
    if (s == 2 && n / i >= (i + 1)) {
      printf("YES\n%d %d %d\n", tab[0], tab[1], n / i);
    } else
      printf("NO\n");
  }
}