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:
import math
def primenum(x):
	count=0
	for i in range(2,int(math.floor(math.sqrt(x)))+1):
		if(x%i==0):
			count=count+1
	if(count==0):
		return True
	else:
		return False
t=int(input())
for i in range(t):
	n=int(input())
	m=n
	if(primenum(n)==True):
		print('NO')
	else:
		l=[]
		for j in range(2,int(math.sqrt(m))+1):
			if(n%j==0):
				l.append(j)
				n=n//j
			if(len(l)==2):
				x=m//(l[0]*l[1])
				if(x>l[0] and x>l[1]):
					l.append(x)
			if(len(l)==3):
				if((l[0]*l[1]*l[2])==m):
					print('YES')
					print(l[0],l[1],l[2])
					break
		else:
			print('NO')