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 div(n):
	s = set()
	for i in range(2, int(n**.5)+2):
		if n % i == 0:
			s.add(i)
			s.add(n // i)
	return s

t = int(input())
for _ in range(t):
	n = int(input())
	s = list(div(n))
	s.sort()
	if len(s) > 2:
		found = 0
		a = b = c = 0
		d = len(s)
		for i in range(d):
			for j in range(i + 1, d):
				if n % (s[i] * s[j]) == 0:
					g = n // (s[i] * s[j])
					if g != s[i] and g != s[j] and g >= 2:
						found = 1
						a = s[i]
						b = s[j]
						c = g
						break
			if found:
				break
		if found:
			print('YES')
			print(a, b, c)
		else:
			print('NO')
	else:
		print('NO')