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:
'''input
5
64
32
97
2
12345
'''
def chay(a,n):
	i = a
	while i*i <= n:
		if n%i == 0:
			b = i
			c = int(n/i)
			if b == c:
				return(0,0)
			else:
				return(b,c)
		i+=1
	return(0,0)


def ktra(n):
	i = 2
	while i*i <= n:
		if n%i == 0:
			a = i
			b, c = chay(a+1,int(n/i))
			if b != 0:
				return (1,a,b,c)
			break
		i+=1
	return(0,0,0,0)
	

for i in range(int(input())):
	n = int(input())
	kq, a, b, c = ktra(int(n))
	if kq == 1:
		print('YES')
		print(a,b,c)
	else:
		print('NO')