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<iostream>
#include<vector>
#include<string>
#include<algorithm>
using namespace std;
int main()
{
   int t;
   cin>>t;
   while(t--)
   {
       int n,i,c1=0;
       cin>>n;
       int c2 = 1;
       vector<int> a(n);
       vector<int> a1(n);
       for(i=0;i<n;i++)
       cin>>a[i];
       if(n%2==0)
       {
       for(i=0;i<n/2;i++)
       {
           a1[c1] = a[i];
           c1 = c1+2;
       }
       for(i=n-1;i>=n/2;i--)
       {
           a1[c2] = a[i];
           c2 = c2+2;
       }
       }
       if(n%2!=0)
       {
       for(i=0;i<=n/2;i++)
       {
           a1[c1] = a[i];
           c1 = c1+2;
       }
       for(i=(n-1);i>n/2;i--)
       {
           a1[c2] = a[i];
           c2 = c2+2;
       }
       }
       for(i=0;i<n;i++)
       cout<<a1[i]<<" ";
       cout<<endl;
   }
   
}