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 fin(n):
	for a in range(2,int(n**(1/3))+1):
		if n%a==0:
			x=n/a
			for b in range(2,int(x**(1/2))+1):
				if x%b==0:
					y=int(x/b)
					if a!=b and b!=y and y!=a:
						return a,b,y
	return 0,0,0
 
 
for _ in range(int(input())):
	n=int(input())
	p,q,r=0,0,0
	p,q,r=fin(n)
	if p!=0:
		print("YES")
		print(p,q,r)
	else:
		print("NO")