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:
#https://codeforces.com/problemset/problem/1294/C
from math import sqrt
for _ in range(int(input())):
	n=int(input())
	f=0
	for i in range(2,int(sqrt(n))+1):
		if n%i==0:
			if n//i != i:
				t=n//i
				for j in range(2,int(sqrt(t))+1):
					if t%j==0:
						if t//j !=j:
							if i!=j and i!=t//j:
								print('YES')
								print(i,j,t//j)
								f=1
								break
		if f:
			break
	if not f:
		print('NO')