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):
	used = []
	n = int(input())
	for i in range(2,round(n/2)):
		if i*i>=n: break
		if n%i==0 and (i not in used):
			used.append(i)
			n=n/i
			break
	for i in range(2,round(n/2)):
		if i*i>=n: break
		if n%i==0 and (i not in used):
			used.append(i)
			n=n/i
			break
	if len(used) < 2 or (n in used) or n==1:
		print("NO")
	else:
		print("YES")
		used.append(int(n))
		for item in used:
			print(item, end=" ")
		print()