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 d[1000001] = {0};
int sum[1000001] = {0};
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int a = -1, b = -1, c;
    for (int i = 2; i <= sqrt(n); i++) {
      if (n % i == 0 && a == -1) {
        a = i;
      } else if (a != -1 && (n / a) % i == 0) {
        b = i;
        break;
      }
    }
    c = n / (a * b);
    if (c == 1 || b == -1 || c == b || c == a) a = -1;
    if (a == -1)
      cout << "NO\n";
    else
      cout << "YES"
           << "\n"
           << a << ' ' << b << ' ' << c << endl;
  }
}