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, a, b, c;
bool solve() {
  cin >> n;
  int i = 2;
  for (i = 2; i * i < n; i++) {
    if (n % i == 0) {
      n /= i;
      a = i;
      break;
    }
  }
  for (int j = 2; j * j < n; j++) {
    if (j == i) continue;
    if (n % j == 0) {
      b = j;
      c = n / j;
      return 1;
    }
  }
  return 0;
}
int main() {
  int tc;
  cin >> tc;
  while (tc--) {
    if (solve()) {
      cout << "YES\n";
      cout << a << ' ' << b << ' ' << c << endl;
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}