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 primefactor(n):
	l = []
	while n%2==0:
		l.append(2)
		n = n//2
	for i in range(3,int(n**0.5)+1,2):
		if n % i == 0:
			l.append(i)
			n//=i
	if n>2:
		l.append(n)
	return l

for _ in range(int(input())):
	n = primefactor(int(input()))
	l = []
	if len(n)==3:
		if len(set(n))==3:
			print("YES")
			print(*n)
		else:
			print("NO")
	elif len(n)>3:
		if n[0]==n[1]:
			l.append(n[0])
			l.append(n[1]*n[2])
			c=1
			for i in range(3,len(n)):
				c *= n[i]
			l.append(c)
			if len(set(l))!=3:
				print("NO")
			else:
				print("YES")
				print(*l)
		else:
			l.append(n[0])
			l.append(n[1])
			c=1
			for i in range(2,len(n)):
				c *= n[i]
			l.append(c)
			if len(set(l))!=3:
				print("NO")
			else:
				print("YES")
				print(*l)
	else:
		print("NO")