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:
# _1294c
##########

def productOfThreeNumbers(n, answer=(1, )):
	lengthOfAnswer = len(answer)
	if lengthOfAnswer == 3:
		if n > answer[-1]:
		    return f'YES\n{answer[1]} {answer[2]} {int(n)}'
		return 'NO'
	
	for i in range(answer[-1]+1, int(n**(1/(4-lengthOfAnswer)))+1):
		if not n%i:
			return productOfThreeNumbers(n/i, answer+(i, ))
	
	return 'NO'


nTestCases = int(input())
testCases = [int(input()) for x in range(nTestCases)]
[print(productOfThreeNumbers(testCase)) for testCase in testCases]