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:
import math
t=int(input())
for i in range(t):
	n=int(input())
	flag=0
	for j in range(2,int(pow(n,0.5)+1)):
		if n%j==0:
			n1=n//j
			for k in range(j+1,int(pow(n1,0.5)+1)):
				n2=n1//k
				if n1%k==0 and n2!=k:
					flag=1
					n2=n1//k
					print("YES")
					print(j,end=" ")
					print(k,end=" ")
					print(n2)
					break
			break
	if flag==0:
		print("NO")