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:
from math import sqrt
T = int(input())
for case in range(T):
	n = int(input())
	ans = False
	move = True
	for i in range(2,int(sqrt(n)) + 1):
		if move is False:break
		if n%i == 0:
			a = i
			b = int(n/a)
			for j in range(a + 1 , int(sqrt(n)) + 1):
				if (b%j == 0):
					b = b//j
					c = j
					if (c==b or c==a or a==b):ans = False
					else:
						move = False
						ans = True
						break
	if ans is True:
		print("YES")
		print(a,b,c)
	else:print("NO")