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:
'''input
3
1 2
3 4
5 6

'''

import math 

# Method to print the divisors 
def printDivisors(n) : 
	list = [] 
	
	# List to store half of the divisors 
	a = []
	x = n
	for i in range(2, int(math.sqrt(n) + 1)) : 
		
		if (x % i == 0) : 
			a.append(i)
			# i -= 1
			x/=i
		if len(a)==2:
			p = 1
			# for i in range(2,len(a)):
			# 	p*=a[i]
			if x==a[0] or x==a[1]:
				print("NO")
				return
			print("YES")
			print(a[0], end = " ")
			print(a[1], end = " ")
			print(int(x))
			return
	print("NO")

	
		


t = int(input())
# print(t)
for i in range(t):
	a = int(input())
	# print((60-m) + (23-h)*60)
	printDivisors(a)