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;
template <typename T>
void print(set<T> v) {
  for (auto x : v) cout << x << " ";
  cout << endl;
}
set<long long int> count_div(long long int m, long long int j) {
  set<long long int> s;
  for (long long int i = 1; i <= sqrtl(m); i++) {
    if (m % i == 0 && i > j) {
      if (i != m / i && (m / i != j)) {
        s.insert(i);
        s.insert(m / i);
        return s;
      } else
        continue;
    }
  }
  return s;
}
set<long long int> divisors(long long int n) {
  set<long long int> s;
  for (long long int i = 1; i <= sqrtl(n); i++) {
    if (n % i == 0 && i >= 2) {
      if (i != n / i) {
        s = count_div(n / i, i);
        if (s.size() == 2) {
          s.insert(i);
          return s;
        }
      }
    }
  }
  return s;
}
signed main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    set<long long int> s = divisors(n);
    if (s.size() == 3) {
      cout << "YES" << endl;
      print(s);
    } else
      cout << "NO" << endl;
  }
}