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
n = int(input())

for i in range(n):
	deb = t = int(input())
	divs = []
	for j in range(2,round(math.sqrt(t)+1)):
		if t%j==0 and j not in divs:
			divs.append(j)
			t //= j
			if len(divs) == 2:
				divs.append(t)
				break
	if len(set(divs)) == 3 and deb == divs[0]*divs[1]*divs[2]:
		print("YES")
		print(divs[0],divs[1],divs[2])
	else:
		print("NO")