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:
I  = input
for _ in [0]*int(I()):
	temp = int(I())
	ans = []
	for i in range(2,temp,1):
		if(temp % i == 0):
			ans.append(i)
			break
		elif i *i > temp:
			break
	if(len(ans) == 0 or ans[0]*ans[0] >= temp):
		print("NO");continue
	temp //= ans[0]
	for i in range(ans[0],int(temp),1):
		if(int(temp) % i == 0 and i != ans[0]):
			ans.append(i)
			temp //= i
			break
		elif i *i > temp:
			break
	if(len(ans) == 1):
		print("NO");continue
	if(int(temp) != ans[0] and int(temp) != ans[1]):
		ans.append(int(temp))
		print("YES")
		for i in ans:
			print(i,end = ' ')
		print('')
	else:
		print("NO")