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