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 prime(n) : 
    if (n <= 1) : 
        return False
    if (n <= 3) : 
        return True
    if (n % 2 == 0 or n % 3 == 0) : 
        return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True
  
t=int(input())
for i in range(t):
	n=int(input())
	if(prime(n)):
		print("NO")
	else:
		flag=0
		ans=[]
		for i in range(2,int(math.sqrt(n))+1):
			if(flag==1):
				break
			if(n%i)==0:
				if (prime(i)==False ):
					a=n/i
					for j in range(2,int(math.sqrt(i))+1):
						if(i%j==0 and a!=j and a!=i//j and j!=i//j):
							b=j
							c=i//j
							flag=1
							break
					break
				elif (prime(n//i)==False ):
					x=n//i
					a=i
					for j in range(2,int(math.sqrt(x))+1):
						if(x%j==0 and a!=j and a!=x//j and j!=x//j):
							b=j
							c=x//j
							flag=1
							break
					break
				else:
					flag=0
		if(flag==0):
			print("NO")
		else:
			print("YES")
			print(a,b,c)