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() {
  long long int t, n, a, b, i, ra, rb, rc;
  cin >> t;
  while (t--) {
    ra = rb = rc = 1;
    cin >> a;
    b = sqrt(a);
    for (i = 2; i <= b + 1; i++) {
      if (a % i == 0) {
        a = a / i;
        ra = i;
        break;
      }
    }
    b = sqrt(a);
    for (i = 2; i <= b + 1 && ra != 1; i++) {
      if (a % i == 0 && i != ra) {
        a = a / i;
        rb = i;
        break;
      }
    }
    if (a != ra && a != rb) rc = a;
    if (ra == 1 || rb == 1 || rc == 1)
      cout << "NO\n";
    else {
      cout << "YES\n";
      cout << ra << " " << rb << " " << rc << endl;
    }
  }
}