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 
import math

def num_divisors(n):
	div=[]
	for i in range(2,int(math.sqrt(n))):
		if n%i==0:
			div.append(i)
			for j in range(i+1,int(math.sqrt(n/i))+1):
				if (n/i)%j==0:
					if (n/i)!=j*j:
						div.extend([j,n/(i*j)])
						print("YES")
						print(" ".join([str(round(d)) for d in div]))
						return
			div.remove(i)
	print('NO')
	
t= int(input())
for i in range(t):
	n= int(input())
	num_divisors(n)