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())
from math import *
import bisect
for i in range(t):
	n = int(input())
	x = set()
	for j in range(2,int(sqrt(n))+1):
		if(n%j==0):
			x.add(j)
		if(n%(n//j)==0):
			x.add(n//j)
	x = list(x)
	x.sort()
	flag = 0
	for j in range(len(x)):
		for k in range(j+1,len(x)):
			y = n/(x[j]*x[k])
			if(y in x and y!=x[j] and y!=x[k]):
				flag = 1
				print('YES')
				print(x[j],x[k],int(y))
				break
		if(flag==1):
			break
	if(flag == 0):
		print('NO')