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:
import math
t = int(input())

for i in range(t):
	n = int(input())
	li = []
	
	n_ = math.ceil(n** 0.5)
	for j in range(2,n_):
		if n % j == 0:
			li.append(j)
			n = n // j
	if n != 1:
		li.append(n)		

	if len(li) <= 2:
		print("NO")

	else:
		w1 = li[0]
		w2 = li[1]
		w3 = 1
		for k in range(2,len(li)):
			w3 = w3 * li[k]

		if w1 != w2 and w2 != w3 and w3 != w1:	
			print("YES")
			print(str(w1) + " " + str(w2) + " " + str(int(w3)))			

		else:
			print("NO")