JJ gives you a number N and challenges you to construct a permutation P of length N such that:
|P_{i + 1} - P_{i}| ≥ 2 for all 1 ≤ i ≤ N - 1 (Here |x| denotes the absolute value of x)

Can you complete JJ's challenge?

As a reminder, a permutation of length N is an array where every integer from 1 to N occurs exactly once.

------ Input Format ------ 

- The first line contains a single integer T — the number of test cases. Then the test cases follow.
- The first and only line of each test case contains one integer N — the length of the permutation P to be constructed.

------ Output Format ------ 

For each test case, output N space-separated integers P_{1}, P_{2}, \ldots, P_{N} denoting the permutation P which satisfies the given conditions.

If no such permutation exists, output -1.

If there are multiple answers, print any.

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{5}$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

----- Sample Input 1 ------ 
2
2
6

----- Sample Output 1 ------ 
-1
1 4 2 5 3 6

----- explanation 1 ------ 
Test Case 1: It can be proven that no permutation of length $2$ exists that satisfies the given conditions.

Test Case 2: $[1, 4, 2, 5, 3, 6]$ satisfies the given condition, since $|P_{i + 1} - P_{i}| ≥ 2$ for all $1 ≤ i ≤ N - 1$

Difficulty: EASY

Solutions:
for _ in range(int(input())):
	n = int(input())
	if n < 4:
		print(-1)
	elif n == 4:
		print('3 1 4 2')
	elif n == 5:
		print('3 1 4 2 5')
	else:
		(i, j) = (1, (n + 1) // 2 + 1)
		while n > 0:
			if n == 1:
				print(i, end='')
			else:
				print(i, j, end=' ')
			i += 1
			j += 1
			n -= 2
		print()


for tc in range(int(input())):
	n = int(input())
	i = 1
	p = list(range(1, n + 1))
	a = []
	odd = 0
	if n % 2 == 0:
		mid = n // 2
	else:
		odd = 1
		mid = n // 2 + 1
	if n <= 3:
		print(-1)
	elif n == 4:
		print(2, 4, 1, 3)
	else:
		for i in range(n // 2):
			a.append(p[i])
			a.append(p[i + mid])
		if odd == 1:
			a.append(p[n // 2])
		print(*a)


t = int(input())
for t in range(t):
	n = int(input())
	if n <= 3:
		print(-1)
	elif n == 4:
		print('2 4 1 3')
	else:
		s = []
		a = 1
		b = n - n // 2 + 1
		for i in range(1, n + 1):
			if i % 2 == 1:
				s.append(str(a))
				a += 1
			else:
				s.append(str(b))
				b += 1
		print(' '.join(s))


import math
t = int(input())
for i in range(t):
	n = int(input())
	if n < 4:
		print(-1)
	elif n == 4:
		print('2 4 1 3')
	else:
		d = math.ceil(n / 2)
		for i in range(1, d + 1):
			print(i, end=' ')
			if d + i <= n:
				print(d + i, end=' ')


t = int(input(''))
if 1 <= t <= 10 ** 5:
	for _ in range(t):
		n = int(input(''))
		if 2 <= n <= 10 ** 5:
			if n < 4:
				print(-1)
			elif n == 4:
				print('3 1 4 2')
			else:
				z = 1
				a = []
				y = int(n / 2 + 0.5)
				x = 1
				for i in range(y):
					a.append(x)
					x += 1
				for i in range(1, n, 2):
					a.insert(i, x)
					x += 1
				for x in a:
					print(x, end=' ')


for z in range(int(input())):
	n = int(input())
	l = []
	l.append(1)
	if n % 2 == 0:
		a = n // 2
		b = a - 1
	else:
		b = n // 2
		a = b + 1
	if n < 4:
		print(-1)
	elif n == 4:
		print('2 4 1 3')
	elif n % 2 == 1:
		for i in range(1, n, 2):
			l.append(l[i - 1] + a)
			l.append(l[i] - b)
		for y in range(len(l)):
			print(l[y], end=' ')
	else:
		for i in range(1, n - 1, 2):
			l.append(l[i - 1] + a)
			l.append(l[i] - b)
		l.append(l[n - 2] + a)
		for y in range(len(l)):
			print(l[y], end=' ')


from itertools import permutations
casos = int(input())
for i in range(casos):
	numero = int(input())
	if numero <= 3:
		print('-1')
	elif numero == 4:
		print('2 4 1 3 ')
	else:
		lista = [0] * numero
		k = 1
		for i in range(0, numero, 2):
			lista[i] = k
			k += 1
		for i in range(1, numero, 2):
			lista[i] = k
			k += 1
		for i in lista:
			print(i, end=' ')


tc = int(input())
for _ in range(tc):
	n = int(input())
	if n <= 3:
		print('-1')
	elif n == 4:
		print('3 1 4 2')
	else:
		arr = [0] * n
		if n % 2 == 0:
			for i in range(1, n // 2 + 1):
				arr[2 * i - 2] += i
			for i in range(n // 2 + 1, n + 1):
				j = i - n // 2
				arr[2 * j - 1] += i
		else:
			for i in range(1, n // 2 + 2):
				arr[2 * i - 2] += i
			for i in range(n // 2 + 2, n + 1):
				j = i - n // 2 - 1
				arr[2 * j - 1] += i
		for ele in arr:
			print(ele, end=' ')
		print()


t = int(input())
for _ in range(t):
	n = int(input())
	if n <= 3:
		print(-1)
	elif n == 4:
		print('2 4 1 3')
	else:
		result = []
		n1 = n
		if n1 % 2 != 0:
			n1 += 1
		for i in range(1, n1 // 2 + 1):
			result.extend([i, n1 // 2 + i])
		if n1 != n:
			result = result[:-1]
		print(' '.join(map(str, result)))


a = int(input())
for i in range(a):
	b = int(input())
	if b < 4:
		print(-1)
	elif b == 4:
		print('2 4 1 3')
	else:
		c = 1
		d = (b + 1) // 2 + 1
		for j in range(b):
			if j % 2 == 0:
				print(c, end=' ')
				c += 1
			else:
				print(d, end=' ')
				d += 1


t = int(input())
for i in range(t):
	n = int(input())
	p = []
	q = []
	if n <= 3:
		print(-1)
	elif n == 4:
		print('2 4 1 3')
	elif n % 2 == 0 and n != 4:
		m = n // 2
		for i in range(1, m + 1):
			print(i, i + m, end=' ')
	else:
		m = n // 2 + 1
		for i in range(1, m + 1):
			if i != m:
				print(i, i + m, end=' ')
			else:
				print(i)


t = int(input())
for _ in range(t):
	n = int(input())
	if n == 4:
		print(3, 1, 4, 2)
	elif n >= 5:
		cnt = 1
		for i in range(1, n + 1):
			if i % 2 != 0:
				print(cnt, end=' ')
			elif i % 2 == 0 and n % 2 != 0:
				print(n // 2 + cnt + 1, end=' ')
				cnt += 1
			elif i % 2 == 0 and n % 2 == 0:
				print(n // 2 + cnt, end=' ')
				cnt += 1
		print()
	else:
		print(-1)


for i in range(int(input())):
	c = []
	f = []
	a = int(input())
	if a > 4:
		if a % 2 == 1:
			l = list(range(1, a + 1))
			v = l.pop(len(l) // 2)
			x = int((len(l) - 2) / 2)
			y = [0] + list(range(1, x + 1, 1)) + list(range(-x, 0, 1))
			y.append(0)
			k = list(range(0, a - 1))
			for i in range(a - 1):
				c.append(y[i] + k[i])
			s = l.copy()
			for i in range(a - 1):
				l[c[i]] = s[i]
			print(*[v] + l)
		else:
			l = list(range(1, a + 1))
			x = int((len(l) - 2) / 2)
			y = [0] + list(range(1, x + 1, 1)) + list(range(-x, 0, 1))
			y.append(0)
			k = list(range(0, a))
			for i in range(a):
				c.append(y[i] + k[i])
			s = l.copy()
			for i in range(a):
				l[c[i]] = s[i]
			print(*l)
	elif a == 4:
		print(*[3, 1, 4, 2])
	else:
		print(-1)


def makepermuation(num):
	if num < 4:
		result = [-1]
	elif num == 4:
		result = [3, 1, 4, 2]
	elif num % 2 == 0:
		result = []
		half_num = int(num / 2)
		for i in range(1, half_num + 1):
			result.append(i)
			result.append(i + half_num)
	else:
		result = []
		half_num = num // 2 + 1
		for i in range(1, half_num + 1):
			result.append(i)
			result.append(i + half_num)
		result.pop()
	return result
T = int(input())
for k in range(T):
	N = int(input())
	ans = makepermuation(N)
	res = ''
	for n in ans:
		res += str(n)
		res += ' '
	res = res[:-1]
	print(res)


for _ in range(int(input())):
	n = int(input())
	if n < 4:
		print(-1)
	elif n == 4:
		print(3, 1, 4, 2, sep=' ')
	else:
		l = [int(x) for x in range(1, n + 1)]
		if n % 2 == 0:
			l1 = l[:n // 2]
			l2 = l[n // 2:]
		else:
			l1 = l[:n // 2 + 1]
			l2 = l[n // 2 + 1:]
		l3 = []
		for x in range(n):
			try:
				if l1[x]:
					l3.append(l1[x])
				if l2[x]:
					l3.append(l2[x])
			except:
				pass
		print(*l3)


t = int(input())
for i in range(t):
	n = int(input())
	if n < 4:
		print(-1)
	elif n == 4:
		print('3 1 4 2')
	else:
		m = 0
		if n % 2 == 0:
			m = n // 2
		else:
			m = n // 2 + 1
		l1 = [x for x in range(1, m + 1)]
		l2 = [x for x in range(m + 1, n + 1)]
		s = ' '.join((f'{x} {y}' for (x, y) in zip(l1, l2)))
		if n % 2 != 0:
			s += ' ' + str(l1[-1])
		print(s)