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 solution(s):
	nums = []
	i = 2
	while len(nums) < 2 and i ** 2 <= s:
		if s % i == 0 and i not in nums:
			nums.append(i)
			s //= i
		i += 1
	if s not in nums and len(nums) == 2:
		print("YES")
		print(*nums, s)
	else:
		print("NO")
t = int(input())

while t > 0:
	t -= 1
	s = int(input())
	solution(s)