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;
using namespace std;
string chk[10] = {"1110111", "0010010", "1011101", "1011011", "0111010",
                  "1101011", "1101111", "1010010", "1111111", "1111011"};
void solve() {
  long long n;
  cin >> n;
  for (int a = 2; a * (a + 1) * (a + 2) <= n; a++)
    if (n % a == 0) {
      int num = n / a;
      for (int b = a + 1; b * (b + 1) <= num; b++)
        if (num % b == 0) {
          int c = num / b;
          printf("YES\n");
          printf("%d %d %d\n", a, b, c);
          return;
        }
    }
  printf("NO\n");
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}