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:
t = int(input())
while t:
	n = int(input())
	i = 2
	a = 0
	while i*i<=n:
		if n%i==0:
			a=i
			n=n/i
			break
		i+=1
	i =2 
	b =0 
	while i*i<=n:
		if n%i==0 and a!=i:
			b= i
			n=n/i
			c = n
			break
		i+=1
	if(a>=2 and b>=2 and c>=2 and c!=b and c!=a):
		print("YES")
		print(int(a),int(b),int(c))
	else:
		print("NO")
	t-=1