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>
int main() {
  int t;
  std::cin >> t;
  for (; t > 0; t--) {
    long n;
    std::cin >> n;
    int i = 2;
    std::vector<int> primes;
    while (i * i <= n) {
      if (n % i == 0) {
        while (n % i == 0) {
          primes.push_back(i);
          n /= i;
        }
      }
      i++;
    }
    if (n != 1) {
      primes.push_back(n);
    }
    if (primes.size() < 3) {
      std::cout << "NO\n";
      continue;
    }
    long a = primes[0];
    long b = primes[1];
    int next_prime = 2;
    if (a == b) {
      b *= primes[next_prime++];
    }
    if (primes.size() <= next_prime) {
      std::cout << "NO\n";
      continue;
    }
    long c = primes[next_prime++];
    while (next_prime < primes.size()) {
      c *= primes[next_prime++];
    }
    if (c == a or c == b) {
      std::cout << "NO\n";
    } else {
      std::cout << "YES\n";
      std::cout << a << " " << b << " " << c << "\n";
    }
  }
}