Given is an integer sequence A_1, ..., A_N of length N.

We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from this sequence so that no two adjacent elements are chosen.

Find the maximum possible sum of the chosen elements.

Here \lfloor x \rfloor denotes the greatest integer not greater than x.

Constraints

* 2 \leq N \leq 2\times 10^5
* |A_i|\leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 ... A_N


Output

Print the maximum possible sum of the chosen elements.

Examples

Input

6
1 2 3 4 5 6


Output

12


Input

5
-1000 -100 -10 0 10


Output

0


Input

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


Output

5000000000


Input

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49


Output

295
#include<bits/stdc++.h>
using namespace std;
typedef long long INT;

INT A[200100], n, C[200100][3];

INT f(INT i, INT c){
    if(C[i][c]) return C[i][c];
    INT k;
    if(i+c==n) return A[i];
    if(i>n) return 0;
    k = f(i+2, c) + A[i];
    if(c>0) k = max(k,f(i+3, c-1) + A[i]);
    if(c>1) k = max(k,f(i+4, c-2) + A[i]);

    return C[i][c]=k;
}
int main(){
    INT i;
    cin >>n;
    for(i=1;i<=n;i++) cin >> A[i];
    if(n%2==0) cout << max(f(1, 1),f(2,0));
    else cout <<max(f(1, 2),max(f(2,1),f(3,0)));
}
