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:
for i in range(int(input())):
	n = int(input())
	d = []
	cnt = 2
	a,b,c = 1,1,1
	for i in range(2,int(n**0.5)+1):
		if n%i==0:
			a = i
			break
	
	x = n//a
	for i in range(2,int(x**0.5)+1):
		if x%i==0 and i!=a:
			b = i
			break
	c = n//(a*b)
	if a<b<c and a*b*c==n and min(a,b,c)>1:
		print("YEs\n",a,b,c)
	else:
		print("NO")