You are given an integer N.

Find a permutation P = [P_{1}, P_{2}, \ldots, P_{N}] of the integers \{1, 2, \ldots, N\} such that sum of averages of all consecutive triplets is minimized, i.e. 

\sum_{i=1}^{N-2} \frac{P_{i} + P_{i+1} + P_{i+2}}{3}

is minimized.

If multiple permutations are possible, print any of them.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- The first and only line of each test case contains an integer N, the size of the permutation.

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

For each test case, output on a new line a permutation which satisfies the above conditions.

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

$1 ≤ T ≤ 1000$
$3 ≤ N ≤ 10^{5}$
- The sum of $N$ over all test cases won't exceed $3\cdot 10^{5}$.

----- Sample Input 1 ------ 
2
4
3

----- Sample Output 1 ------ 
3 2 1 4
3 2 1
----- explanation 1 ------ 
Test case $1$: The sum is $\frac{P_{1} + P_{2} + P_{3}}{3} + \frac{P_{2} + P_{3} + P_{4}}{3} = \frac{3 + 2 + 1}{3} + \frac{2 + 1 + 4}{3} = 6/3 + 7/3 = 4.333\ldots$ Among all possible permutations of $\{1, 2, 3, 4\}$, this is one of the permutations which provides the minimum result.

Test case $2$: The sum is $\frac{3+2+1}{3} = 6/3 = 2$. Every permutation of size $3$ will have this value, hence it is the minimum possible.

Difficulty: MEDIUM

Solutions:
for _ in range(int(input())):
	N = int(input())
	if N == 3:
		print('3 2 1')
	elif N == 4:
		print('3 2 1 4')
	else:
		arr = [0] * N
		for i in range(2, N - 2):
			arr[i] = i - 1
		arr[0] = N
		arr[-1] = N - 1
		arr[1] = N - 2
		arr[-2] = N - 3
		print(' '.join((str(x) for x in arr)))


for _ in range(int(input())):
	n = int(input())
	if n > 3:
		print(n - 1, n - 2, end=' ')
		for i in range(1, n - 2):
			print(i, end=' ')
		print(n)
	elif n == 3:
		print(3, 2, 1)
	elif n == 2:
		print(1, 2)
	else:
		print(1)


trials = int(input())
for i in range(trials):
	size = int(input())
	if size == 3:
		print('3 2 1')
		continue
	elif size == 4:
		print('3 2 1 4')
		continue
	first_two = ' '.join((str(x) for x in [size, size - 2]))
	middle = ' ' + ' '.join((str(x) for x in range(1, size - 3)))
	last_two = ' ' + ' '.join((str(x) for x in [size - 3, size - 1]))
	print(first_two + middle + last_two)


t = int(input())
for i in range(t):
	n = int(input())
	l = list()
	if n > 4:
		l.extend([n, n - 2, n - 3, n - 1])
		for k in range(4, n):
			l.insert(k - 2, n - k)
		for p in l:
			print(p, end=' ')
	elif n == 4:
		print('3 2 1 4')
	elif n == 3:
		print('3 2 1')