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 JAVA):

Solution:

import java.util.*;

public class test {
	static int N = (int) 2e5 + 99;

	public static class pair implements Comparable<pair> {
		int x;
		int s;

		public pair(int x, int s) {
			this.x = x;
			this.s = s;
		}

		@Override
		public int compareTo(pair o) {
			return (this.s - o.s);
		}
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		StringBuilder st = new StringBuilder();
		while (t-- > 0) {
			int n=sc.nextInt();
			HashSet<Integer> hs=solve(n);
			if(hs.contains(1))hs.remove(1);
			if(hs.size()>=3) {System.out.println("YES");
			for(Integer val: hs ) {
				System.out.print(val+" ");
			}
			System.out.println();
			}
			else System.out.println("NO");
			
		}
		
		System.out.println(st);
		

	}

	static HashSet<Integer> solve(int n) {
		HashSet<Integer> hs=new HashSet<>();
		int i = 2, j = 0;
		int N=n;
		while (i <= Math.sqrt(n)) {
			if (hs.size()==2)
				break;
			if (N % i == 0) {
				hs.add(i);
				N = N/ i;
			}
			i++;
		}
		hs.add(N);
		return hs;

	}
}