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 MOD = 1000000007;
const int N = 1000002;
const double PI = 4 * atan(1);
const double eps = 1e-7;
const long long oo = 1e18;
vector<pair<long long, long long> > v;
long long t;
long long n;
int main() {
  ios::sync_with_stdio(0);
  cin >> t;
  while (t--) {
    cin >> n;
    vector<long long> v;
    long long x = sqrt(n);
    for (int i = 2; i <= x; i++) {
      if (n % i == 0) {
        v.push_back(i);
        n /= i;
        if (v.size() == 2) break;
      }
    }
    if (n >= 2 && v.size() == 2 && n != v[0] && n != v[1]) {
      cout << "YES\n";
      cout << v[0] << " " << v[1] << " " << n << endl;
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}