You are given a positive integer $n$. Your task is to find any three integers $a$, $b$ and $c$ ($0 \le a, b, c \le 10^9$) for which $(a\oplus b)+(b\oplus c)+(a\oplus c)=n$, or determine that there are no such integers.

Here $a \oplus b$ denotes the bitwise XOR of $a$ and $b$. For example, $2 \oplus 4 = 6$ and $3 \oplus 1=2$.


-----Input-----

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The following lines contain the descriptions of the test cases.

The only line of each test case contains a single integer $n$ ($1 \le n \le 10^9$).


-----Output-----

For each test case, print any three integers $a$, $b$ and $c$ ($0 \le a, b, c \le 10^9$) for which $(a\oplus b)+(b\oplus c)+(a\oplus c)=n$. If no such integers exist, print $-1$.


-----Examples-----

Input
5
4
1
12
2046
194723326
Output
3 3 1
-1
2 4 6
69 420 666
12345678 87654321 100000000


-----Note-----

In the first test case, $a=3$, $b=3$, $c=1$, so $(3 \oplus 3)+(3 \oplus 1) + (3 \oplus 1)=0+2+2=4$.

In the second test case, there are no solutions.

In the third test case, $(2 \oplus 4)+(4 \oplus 6) + (2 \oplus 6)=6+2+4=12$.

Difficulty: EASY

Solutions:
import sys

def parse_next_line():
	test_str = sys.stdin.readline()
	return int(test_str)

def main(_):
	num_inputs = int(sys.stdin.readline())
	for _ in range(num_inputs):
		num = parse_next_line()
		if num % 2 != 0:
			print(-1)
		else:
			print(0, num // 2, num // 2)
main(sys.argv[1:])


import sys
input = sys.stdin.readline
t = int(input())
for t in range(t):
	n = int(input())
	if n % 2 != 0:
		print(-1)
	else:
		a = 0
		b = n // 2
		c = n - b
		print(a, b, c)


for s in [*open(0)][1:]:
	s = int(s)
	print(-1) if s & 1 else print(0, s // 2, s // 2)


import sys
input = sys.stdin.readline

def sol():
	n = int(input())
	if n & 1:
		return [-1]
	return [0, n >> 1, n >> 1]
for _ in range(int(input())):
	print(*sol())


t = int(input())
for i in range(t):
	x = int(input())
	if x % 2 == 1:
		print(-1)
	else:
		print('%d %d %d' % (0, x / 2, x / 2))


t = int(input())
for _ in range(t):
	final = int(input())
	if final % 2 != 0:
		print('-1')
	else:
		half = str(final // 2)
		print('0 ' + half + ' ' + half)