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 Product_of_Three_Numbers
{
public static void main(String args[])
{
Scanner ob=new Scanner(System.in);
int t=ob.nextInt();
while(t-->0)
{
int n=ob.nextInt();
int a=0,b=0;
for(int i=2;i*i<n;i++)
{
if(n%i==0)
{
n/=i;
if(a==0)
a=i;
else{
b=i;
break;
}
}
}
if(a!=0 && b!=0 && n>b) {
System.out.println("YES");
System.out.println(a+" "+b+" "+n+" ");}
else
				System.out.println("NO");
			}
}
}