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

t = int(input())

for xx in range(t):
	n = int(input())
	i = 2
	fl = 0
	divs = []
	while(i*i <= n):
		if n%i == 0:
			divs.append(i)
			n//=i
		if len(divs) == 2:
			break
		i += 1
	if len(divs) < 2: fl = 1
	if fl == 1:
		print("NO")
		continue
	kr = n
	if kr == 1 or kr == divs[0] or kr == divs[1]:
		print("NO")
		continue
	else:
		divs.append(kr)
		print("YES")
		print(" ".join([str(v) for v in divs]))