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 math import sqrt
t = int(input())
for i in range(t):
	n = int(input())
	sol = {}
	j = 2
	sqroot = {}
	sqroot[n] = int(sqrt(n))
	while(j<=sqroot[n]):
		if len(sol)==2:
			break
		if n%j==0:
			sol[j] = 1
			n = n//j
			sqroot[n] = int(sqrt(n))
		j += 1
	if len(sol)==2 and (n not in sol):
		print("YES")
		for j in sol:
			print(j,end=" ")
		print(n)
	else:
		print("NO")