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 i in range(t):
	n = int(input())
	p = []
	j = 2
	while j * j <= n:
		while (n % j == 0):
			p.append(j)
			n //= j
		j += 1
	if n > 1:
		p.append(n)
	if len(p) < 3:
		print("NO")
	elif len(p) == 3:
		if p[0] != p[1] and p[1] != p[2] and p[0] != p[2]:
			print("YES")
			print(p[0], p[1], p[2])
		else:
			print("NO")
	else:
		mult = 1
		for x in p:
			mult *= x
		a = p[0]
		b = -1
		for x in p:
			if x != a:
				b = x
				break
		if b != -1:
			print("YES")
			print(a, b, mult // a // b)
		elif len(p) >= 6:
			print("YES")
			print(p[0], p[1] * p[2], mult // p[0] // p[1] // p[2])
		else:
			print("NO")