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 <iostream>
#include <algorithm>
using namespace std;

int main()
{
    int n,cur;
    cin >> n;
    long long ans = 0;
    cin >> cur;
    long long tot[3] = { 0,0,cur };
    for (int i = 2; i <= n; i++) {
        cin >> cur;
        if (i % 2) {
            tot[1] = max(tot[1], tot[2]);
            tot[0] += cur;
            tot[2] += cur;
        }
        else {
            tot[0] = max(tot[0], tot[1]);
            tot[1] += cur;
        }
    }
    cout << (n % 2 ? max(tot[0], tot[1]) : max(tot[1], tot[2]));
}