Statement : A. Construct an Array

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.

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 $n$ ($1 \le n \le 500$).

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.

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.