A. Favorite Sequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Polycarp has a favorite sequence $a[1 \dots n]$ consisting of $n$ integers. He wrote it out on the whiteboard as follows:

• he wrote the number $a_1$ to the left side (at the beginning of the whiteboard);
• he wrote the number $a_2$ to the right side (at the end of the whiteboard);
• then as far to the left as possible (but to the right from $a_1$), he wrote the number $a_3$;
• then as far to the right as possible (but to the left from $a_2$), he wrote the number $a_4$;
• Polycarp continued to act as well, until he wrote out the entire sequence on the whiteboard. The beginning of the result looks like this (of course, if $n \ge 4$).

For example, if $n=7$ and $a=[3, 1, 4, 1, 5, 9, 2]$, then Polycarp will write a sequence on the whiteboard $[3, 4, 5, 2, 9, 1, 1]$.

You saw the sequence written on the whiteboard and now you want to restore Polycarp's favorite sequence.

Input

The first line contains a single positive integer $t$ ($1 \le t \le 300$) — the number of test cases in the test. Then $t$ test cases follow.

The first line of each test case contains an integer $n$ ($1 \le n \le 300$) — the length of the sequence written on the whiteboard.

The next line contains $n$ integers $b_1, b_2,\ldots, b_n$ ($1 \le b_i \le 10^9$) — the sequence written on the whiteboard.

Output

Output $t$ answers to the test cases. Each answer — is a sequence $a$ that Polycarp wrote out on the whiteboard.

Example
Input
6
7
3 4 5 2 9 1 1
4
9 2 7 1
11
8 4 3 1 2 7 8 7 9 4 2
1
42
2
11 7
8
1 1 1 1 1 1 1 1

Output
3 1 4 1 5 9 2
9 1 2 7
8 2 4 4 3 9 1 7 2 8 7
42
11 7
1 1 1 1 1 1 1 1

Note

In the first test case, the sequence $a$ matches the sequence from the statement. The whiteboard states after each step look like this:

$ \Rightarrow [3, 1] \Rightarrow [3, 4, 1] \Rightarrow [3, 4, 1, 1] \Rightarrow [3, 4, 5, 1, 1] \Rightarrow [3, 4, 5, 9, 1, 1] \Rightarrow [3, 4, 5, 2, 9, 1, 1]$.