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:
t=int(input())

for _ in range(t):
	n=int(input())
	ad=False
	for i in range(2,10001):
		if (n%i==0):
			ln1=n//i
			n1=i
			#print("n1 = ",n1)
			for j in range(i+1,10001):
				#print("ln1(rem)j = ",ln1%j)
				if (ln1%j==0 and j*j!=ln1 and ln1//j!=i and ln1//j!=1):
					ln2=ln1//j
					n2=j
					n3=ln2
					print("YES")
					print(n1,n2,n3)
					ad=True
					break
				if (ad==True):
					break
			if (ad==True):
				#print("NO")
				break
		if (ad==True):
			break

	if (ad==False):
		print("NO")