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:
def solve(x):
	factors = []
	i = 2
	while i*i < x:
		if x % i == 0:
			x //= i
			factors.append(i)
			if len(factors) == 2:
				break
		i += 1
	factors.append(x)
	if len(factors) == 3:
		print("YES")
		print(f"{factors[0]} {factors[1]} {factors[2]}")
	else:
		print("NO")

def main():
	t = int(input())
	for i in range(t):
		x = int(input())
		solve(x)

main()