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:

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