You are given an integer $n$. Find a sequence of $n$ integers $a_1, a_2, \dots, a_n$ such that $1 \leq a_i \leq 10^9$ for all $i$ and $$a_1 \oplus a_2 \oplus \dots \oplus a_n = \frac{a_1 + a_2 + \dots + a_n}{n},$$ where $\oplus$ represents the bitwise XOR .

It can be proven that there exists a sequence of integers that satisfies all the conditions above.


-----Input-----

The first line of input contains $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first and only line of each test case contains one integer $n$ ($1 \leq n \leq 10^5$) — the length of the sequence you have to find.

The sum of $n$ over all test cases does not exceed $10^5$.


-----Output-----

For each test case, output $n$ space-separated integers $a_1, a_2, \dots, a_n$ satisfying the conditions in the statement.

If there are several possible answers, you can output any of them.


-----Examples-----

Input
3
1
4
3
Output
69
13 2 8 1
7 7 7


-----Note-----

In the first test case, $69 = \frac{69}{1} = 69$.

In the second test case, $13 \oplus 2 \oplus 8 \oplus 1 = \frac{13 + 2 + 8 + 1}{4} = 6$.

Source: codeforces | Difficulty: EASY
Tags: Constructive algorithms


Solutions:
for n in [int(input()) for _ in range(int(input()))]:
	print(' '.join(['2' if n % 2 or i > 1 else '1' if i == 0 else '3' for i in range(n)]))


for _ in range(int(input())):
	s = int(input())
	ans = []
	if s % 2 == 0:
		ans = ['1', '3'] + ['2'] * max(s - 2, 0)
	else:
		ans = ['2'] * s
	print(' '.join(ans))


for t in range(int(input())):
	n = int(input())
	if n % 2 == 1:
		print('2 ' * n)
	else:
		print('1 3 ' + '2 ' * (n - 2))


t = int(input())
for i in range(t):
	n = int(input())
	if n % 2 == 0:
		st = '3 ' + '2 ' * (n - 2) + '1'
	else:
		st = '2 ' * (n - 1) + '2'
	print(st)