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, ceil
def s(y, x=0):
	for i in range(2, ceil(sqrt(y))):
		n = y // i
		if y % i == 0 and i != x and n != x and i != n :
			return i, n
	else:
		return 0, 0
for i in range(int(input())):
	x, y = s(int(input()))
	y, z = s(y, x)
	if y == z:
		print('NO')
	else:
		print('YES')
		print(x, y, z)