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 endl '\n'
#define ll long long
#define rint register int
#define minpq priority_queue <int, vector<int>, greater<int> >
#define maxpq  priority_queue <int>

#define re register
#define pb(x) push_back(x);
#define ce(x) cout << x << '\n';

using db = long double;
using pll = pair < ll, ll >;
#define scan(a, n) 		for(int i = 0; i < n; i++)cin >> a[i];

#define rep(i,x,n,inc) for(i=x ; i<n ; i+=inc)
#define repr(i,x,n,inc) for( i=x ; i>n ; i+=inc)
#define all(a)      (a).begin(),(a).end()
#define unique_sort(x) sort(all(x)), x.resize(distance(x.begin(), unique(all(x))))

#define mp(a,b) make_pair(a,b)
#define ff first
#define ss second
#define hell 1000000007
#define infl LLONG_MAX

#define conutBits(n)	__builtin_popcount(n)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Fill(s,v) memset(s,v,sizeof(s))
#define cout_p(x, p) cout << fixed << setprecision((p)) << x << endl     //print with precision

#define tc(tt) \
    ll tt;    \
    cin >> tt; \
    for (ll _tt = 0; _tt < tt; _tt++) // testcase 

int32_t main() {
	ios::sync_with_stdio(0); 		cin.tie(0); cout.tie(0);

	ll t, i, x, j, y, 	z, k, n;
	tc(tt) {
		cin >> n;
		std::vector<ll> v;
		deque<ll> dq;
		while (n--) {
			cin >> x;
			dq.push_back(x);
		}

		bool f = 0;
		while (dq.size()) {
			if (f) {
				x = dq.back();
				dq.pop_back();
			} else {
				x = dq.front();
				dq.pop_front();
			}
			cout << x << " ";
			f ^= 1;
		}

		cout << "\n";
	}
}