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 as m
n = int(input())
for _ in range(n):
	a = int(input())
	v=[]
	for i in range(2,int(m.sqrt(a))+1):
		if a%i==0 and i!=a//i:
			z = a//i
			for j in range(i+1,int(m.sqrt(z))+1):
				if z%j==0 and j!=z//j:
					a = 0
					v.append([i,j,z//j])
					break
		if a==0:
			break
	if a==0:
		print("YES")
		for i in v:
			print(*i)
	else:
		print("NO")