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:

def foo(n):
	x=pow(n,.5)
	x=int(x)+1
	l=[]
	for i in range(2,x):
		if n%i==0:
			z=n//i
			l.append(i)
			if z!=i:
				l.append(z)
	l.sort()
	if len(l)>=3:
		for i in range(0,len(l)-1):
			k=l[i]*l[i+1]
			z=n//k
			if (z in l) and z!=l[i] and z!=l[i+1]:
				print("YES")
				k=[l[i],l[i+1],z]
				print(*k)
				return 
		print("NO")



	else:
		return print("NO")



t=int(input())
for t1 in range(0,t):
	n=int(input())
	foo(n)