You are given a positive integer $n$.

The weight of a permutation $p_1, p_2, \ldots, p_n$ is the number of indices $1\le i\le n$ such that $i$ divides $p_i$. Find a permutation $p_1,p_2,\dots, p_n$ with the minimum possible weight (among all permutations of length $n$).

A permutation is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array) and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 10^4$). The description of the test cases follows.

The only line of each test case contains a single integer $n$ ($1 \leq n \leq 10^5$) — the length of permutation.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.


-----Output-----

For each test case, print a line containing $n$ integers $p_1, p_2,\dots, p_n$ so that the permutation $p$ has the minimum possible weight.

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


-----Examples-----

Input
2
1
4
Output
1
2 1 4 3


-----Note-----

In the first test case, the only valid permutation is $p=[1]$. Its weight is $1$.

In the second test case, one possible answer is the permutation $p=[2,1,4,3]$. One can check that $1$ divides $p_1$ and $i$ does not divide $p_i$ for $i=2,3,4$, so the weight of this permutation is $1$. It is impossible to find a permutation of length $4$ with a strictly smaller weight.

Difficulty: EASY

Solutions:
t = int(input())
ans = []
for _ in range(t):
	n = input()
	s = n + ' '
	for i in range(1, int(n)):
		s += str(i) + ' '
	ans.append(s)
for i in ans:
	print(i)


for _ in range(int(input())):
	vjd = int(input())
	print(vjd, ' '.join([str(i) for i in range(1, vjd)]))


t = int(input())
for i in range(t):
	n = int(input())
	print(''.join([str(n) + ' '] + [str(a) + ' ' for a in range(1, n)]))


for _ in range(int(input())):
	x = int(input())
	print(x, ' '.join([str(i) for i in range(1, x)]))


t = int(input())
for _ in range(t):
	n = int(input())
	print(f"{n} {' '.join((str(i) for i in range(1, n)))}")