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;
vector<long long> v;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long a = 0, b = 0, c, d, e, f = 0, l, g, m, n, k, i, j, t, p, q;
  cin >> t;
  while (t--) {
    cin >> n;
    f = 0;
    v.clear();
    for (i = 2; f < 2 && i <= sqrt(n) + 1; i++) {
      if (n % i == 0) {
        v.push_back(i);
        n /= i;
        f++;
      }
    }
    if (v.size() < 2 || n == 1 || n == v[0] || n == v[1]) {
      cout << "NO\n";
    } else {
      cout << "YES\n" << v[0] << ' ' << v[1] << ' ' << n << '\n';
    }
  }
  return 0;
}