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

def isprime(n):
	if n==1:
		return False
	if n==2:
		return True
	for x in range(2,int(math.sqrt(n))):
		if n%x==0:
			return False
	return True

def issquare(n):
	if int(math.sqrt(n))*int(math.sqrt(n)) == n:
		return True
	else:
		return False

def solve(n):
	for i in range(2,int(math.sqrt(n))):
		if n%i==0:
			if not(isprime(i)):
				x = i
				y = int(n/i)
				for j in range(2,int(math.sqrt(x))+1):
					if x%j == 0 and j != y and x/j != y and j!=x/j:
						print("YES")
						print(str(j) + " " + str(int(x/j)) + " " + str(y))	
						return
			elif not(isprime(n/i)):
				x = n/i
				y = i
				for j in range(2,int(math.sqrt(x))+1):
					if x%j == 0 and j != y and x/j != y and j!=x/j:
						print("YES")
						print(str(j) + " " + str(int(x/j)) + " " + str(y))	
						return
	print("No")

t = int(input())

while t:
	n = int(input())
	solve(n)
	t-=1