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, a;
  cin >> t;
  while (t--) {
    cin >> a;
    int f1 = 0, f2 = 0, rs1, rs2, rs3;
    for (int i = 2; i < min(a, 100000); i++) {
      if (a % i == 0) {
        a = a / i;
        f1 = 1;
        rs1 = i;
        for (int j = i + 1; j < min(a, 100000); j++) {
          if (a % j == 0) {
            a = a / j;
            f2 = 1;
            rs2 = j;
            rs3 = a;
            break;
          }
        }
        break;
      }
    }
    if (f1 == 1 && f2 == 1) {
      if (rs1 < rs2 && rs2 < rs3 && rs1 < rs3) {
        cout << "YES" << endl;
        cout << rs1 << " " << rs2 << " " << rs3 << endl;
      } else {
        cout << "NO" << endl;
      }
    } else {
      cout << "NO" << endl;
    }
  }
  return 0;
}