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;
int main() {
  int T, t;
  cin >> T;
  for (t = 0; t < T; t++) {
    int n, i;
    cin >> n;
    int numPrime = 0;
    int num = n;
    int f = 1;
    vector<int> v;
    map<int, int> mp;
    for (i = 2; i <= sqrt(n); i++) {
      f = 1;
      if (num % i == 0) {
        f = f * i;
        while (num % i == 0) {
          if (f != 1 && mp[f] == 0) {
            v.push_back(f);
            mp[f] = 1;
            f = 1;
          } else {
            f = f * i;
          }
          num = num / i;
        }
      }
    }
    if (mp[num] == 0 && num != 1) {
      v.push_back(num);
      mp[num] = 1;
    }
    if (v.size() == 2) {
      int r = n / (v[0] * v[1]);
      if (mp[r] == 0 && r != 1) v.push_back(r);
    }
    sort(v.begin(), v.end());
    if (v.size() > 2) {
      cout << "YES" << endl;
      cout << v[0] << " " << v[1] << " " << n / (v[0] * v[1]) << endl;
    } else
      cout << "NO" << endl;
  }
  return 0;
}