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 PYTHON3):

Solution:
# your code goes here
import math
t=int(input())
while(t>0):
	n=int(input())
	l=[]
	c=0
	s=int(math.sqrt(n))
	for i in range(2,s+1):
		if(n%i==0):
			l.append(i)
			c+=1
			n=n//i
			break
	for i in range(2,s+1):
		if(i not in l and n%i==0):
			l.append(i)
			c+=1
			n=n//i
			break
	if(c<2 or n==1 or n in l):
		print("NO")
	else :
		print("YES")
		for i in l:
			print(i,end=' ')
		print(n)
	t-=1