Problem: Polycarp has a favorite sequence a[1 ... 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. 

<image> The beginning of the result looks like this (of course, if n ≥ 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 ≤ t ≤ 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 ≤ n ≤ 300) — the length of the sequence written on the whiteboard.

The next line contains n integers b_1, b_2,…, b_n (1 ≤ b_i ≤ 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] ⇒ [3, 1] ⇒ [3, 4, 1] ⇒ [3, 4, 1, 1] ⇒ [3, 4, 5, 1, 1] ⇒ [3, 4, 5, 9, 1, 1] ⇒ [3, 4, 5, 2, 9, 1, 1].

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
 
#define IO          ios_base :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int         long long
#define double      long double
#define vi          vector<int>
#define vvi         vector<vi>
#define pii         pair<int, int>
#define vii         vector<pii>
#define endl        '\n'
#define pb          emplace_back
#define all(v)      (v).begin(), (v).end()
#define rall(v)     (v).rbegin(), (v).rend()
#define mod         1000000007
const int N = 2e5;
int b[N];

void solve()
{
	int n;
	cin >> n;
	for(int i=0;i<n;i++)
	{
		cin >> b[i];
	}
	int d = ceil((double)n/2);
	for(int i=0;i<d;i++)
	{
		if(i == n-1-i)
		{
			cout << b[i] << " ";
		}
		else
		{
			cout << b[i] << " " << b[n-i-1] << " ";
		}
	}
	cout << endl;
}
signed main() {
	IO;
	int t = 1;
	cin >> t;
	while (t--) {
		solve();
	}
}