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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int cases;
  cin >> cases;
  for (int tt = 0; tt < cases; tt++) {
    long long n;
    cin >> n;
    int ok = 0;
    long long ax, ay, az;
    for (long long i = 2; i * i <= n && !ok; i++) {
      if (n % i == 0) {
        for (long long j = 2; j * j <= i && !ok; j++) {
          if (i % j == 0) {
            long long x = i / j;
            long long y = j;
            long long z = n / i;
            if (x != y && y != z && x != z && x > 1 && y > 1 && z > 1) {
              ok = 1;
              ax = x;
              ay = y;
              az = z;
            }
          }
        }
        for (long long j = 2; j * j <= n / i && !ok; j++) {
          if ((n / i) % j == 0) {
            long long x = i;
            long long y = j;
            long long z = n / i / j;
            if (x != y && y != z && x != z && x > 1 && y > 1 && z > 1) {
              ok = 1;
              ax = x;
              ay = y;
              az = z;
            }
          }
        }
      }
    }
    if (ok) {
      cout << "YES" << endl;
      cout << ax << " " << ay << " " << az << endl;
    } else {
      cout << "NO" << endl;
    }
  }
}