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 ll long long
#define rep(i,n) for(i=0;i<n;i++)
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define debug cout<<"debug"<<endl;
#define kk ios::sync_with_stdio(false); cin.tie(0);
ll Pow(ll x,ll y){return y==0?:x*pow(x,y-1);}
ll gcd(ll a, ll b){return (b == 0 ? a : gcd(b, a % b));}
ll lcm(ll a, ll b){return (a * (b / gcd(a, b)));}

int main()
{
     ///"In the name of Allah,most gracious and most merciful"///
    kk;
    ll t;
    cin>>t;
    while(t--)
    {
        ll i,j,x,y,z,count=0,sum=0,n;
        cin>>n;
        ll a[n];
        rep(i,n)
        {
            cin>>a[i];
        }
        for(ll i=0;i<n/2;i++)
        {
            cout<<a[i]<<" "<<a[n-1-i]<<" ";
        }
        if((n%2)!=0)
        cout<<a[n/2]<<endl;
        else
        {
            cout<<endl;
        }
        
    }


    return 0;
}