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 sys
# file = open('test1')
# sys.stdin = file

def ii():
	a = int(input())
	return a
def ai():
	a = list(map(int, input().split()))
	return a
def mi():
	a = map(int, input().split())
	return a


from math import sqrt

def fact(n):
	lst = []
	for i in range(2, int(sqrt(n))+1):
		if n%i==0:
			a = i
			# print(a,"a")
			b = n//i
			for j in range(2, int(sqrt(b))+1):
				# print(j,"j")
				if b%j == 0 and j!=a and (b//j)!=a and j!=(b//j):
					lst.append(a)
					lst.append(j)
					lst.append(b//j)
					return lst


for _ in range(ii()):
	n = ii()
	lst = fact(n)
	if lst:
		print("YES")
		print(*lst)
	else:
		print("NO")