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 
import math as m
def divisor(n):
    arr=[]
    for i in range(2,int(m.sqrt(n))+1):
        if n%i==0:
            arr.append(i)
    return arr

t=int(input())
for _ in range(t):
    n=int(input())
    temp=divisor(n)
    if temp==[]:
        print("NO")
    else:
        a=temp[0]
        n=n//temp[0]
        temp=divisor(n)
        boo=True
        for i in temp:
            if i!=a and n%i==0 and n//i!=a and n//i!=i and n//i!=1:
                print("YES")
                print(a,i,n//i)
                boo=False
                break
        if boo:
            print("NO")
            

   		   		 								   	  			 		