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;
int32_t main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, a, b, bit1 = 0, bit2 = 0;
    cin >> n;
    for (long long i = 2; i * i <= n; i++)
      if (n % i == 0 && i != n / i) {
        a = i;
        b = n / i;
        bit1++;
        break;
      }
    long long x, y;
    for (long long i = 2; i * i <= b; i++)
      if (b % i == 0 && i != b / i && a != i && a != b / i) {
        x = i;
        y = b / i;
        bit2++;
        break;
      }
    if (bit1 != 0 && bit2 != 0) {
      cout << "YES" << endl;
      cout << a << " " << x << " " << y << endl;
    } else
      cout << "NO" << endl;
  }
  return 0;
}