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
for _ in range(int(input())):
	n = int(input())
	d = set()
	for i in range(2, int(math.sqrt(n)) + 1):
		if len(d) >= 2:
			break
		if n % i == 0:
			d.add(i)
			n = n // i
	if len(d) < 2 or n == 1 or n in d:
		print("NO")
	else:
		print("YES")
		for t in d:
			print(t, end = ' ')
		print(n)