A. Construct an Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an integer $$$n$$$. You need to construct an array of integers $$$a_1, a_2, \ldots, a_n$$$ such that the following conditions are satisfied:

  • $$$1 \leq a_i \leq 2 \cdot n$$$ for all $$$i$$$ from $$$1$$$ to $$$n$$$.
  • All elements of the array and the sums of adjacent elements are pairwise distinct. In other words, among the numbers $$$\{a_1, a_2, \ldots, a_n, a_1 + a_2, a_2 + a_3, \ldots, a_{n - 1} + a_n\}$$$, there should not be two equal numbers.
Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The only line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 500$$$).

Output

For each test case, output an array of length $$$n$$$ that satisfies the condition of the problem. It can be shown that such an array always exists under the given constraints.

Example
Input
3
1
3
6
Output
1 
6 2 3
8 1 11 2 3 4
Note

In the second example, all elements and adjacent sums form the set $$$\textbf{6}, \textbf{2}, \textbf{3}, 8, 5$$$, all of whose elements are distinct.

In the third example, all elements and adjacent sums form the set $$$\textbf{8}, \textbf{1}, \textbf{11}, \textbf{2}, \textbf{3}, \textbf{4}, 9, 12, 13, 5, 7$$$, whose elements are also distinct.