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 solve(n,i):
	a=-1
	b=-1
	while (i*i<=n):
		if (n%i)==0:
			a=i
			b=n//i
			if a==b:
				a=-1
				b=-1
			break
		i+=1
	return a,b



for t in range(int(input())):

	n =int(input())

	a,b = solve(n,2)
	if a==-1:
		print("NO")
	else:
		b,c = solve(b,a+1)
		if b==-1:
			print("NO")
		else:
			print("YES")
			print(a,b,c)