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())
for y in range(t):
	n = int(input())
	i = 2
	a = n
	ans = []
	while(i*i <= n):
		if(a%i == 0):
			ans.append(i)
			a //= i
		i += 1
		if len(ans) == 2: break
	if(len(ans) != 2):
		print("NO")
	elif(a == ans[0] or a == ans[1]):
		print("NO")
	else:
		print("YES")
		print(ans[0],ans[1],a)