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:
for _ in range(int(input())):
	n=int(input())
	x=int(n)
	v=2
	k=0
	t=[]
	while n>v*v and k<2:
		if n%v==0:
			t.append(v)
			k+=1
			n=n//v
		v+=1
	if len(t)<2:
		print("NO")
	else:
		k=x//(t[0]*t[1])
		if k==t[0] or k==t[1]:
			print("NO")
		else:			
			print("YES")
			print(t[0],t[1],x//(t[0]*t[1]))