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:
from sys import stdin , stdout
from os import path
if path.exists("input.txt"):
	stdin = open("input.txt",'r')
for _ in range(int(stdin.readline())):
	x = int(stdin.readline())
	i = 2 
	q = []
	while  len(q)< 2 and i*i < x:
		if  x%i == 0 :
			q.append(i)
			x //= i
		i+=1
	if len(q) == 2 and x not in q : 
		print("YES")
		print(*q,x)
	else:
		print("NO")