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;
const int N = (int)998244353;
const int M = (int)1000000007;
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int t;
  cin >> t;
  for (int j = 0; j < t; j++) {
    int n, count = 0, b = 0, c = 0, flag = 0;
    cin >> n;
    for (int i = 2; i <= sqrt(n); i++) {
      if (n % i == 0) {
        c = i;
        n = n / i;
        flag = 1;
        break;
      }
    }
    for (int i = c + 1; i < sqrt(n) + 1 && flag; ++i) {
      if (n % i == 0) {
        b = i;
        n = n / i;
        break;
      }
    }
    if (n == 0 || b == 0 || c == 0 || b == n || c == n)
      cout << "NO"
           << "\n";
    else {
      cout << "YES"
           << "\n";
      cout << c << " " << b << " " << n << "\n";
    }
  }
  return 0;
}