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 <limits>
#include <numeric>

constexpr long small_enough = -2000000001;

int main()
{
    int N;
    std::cin >> N;

    long skip0 = 0;
    auto skip1 = small_enough;
    auto skip2 = small_enough;

    for (auto i = 1; i <= N; i++) {
        long input;
        std::cin >> input;

        if (i % 2 == 0) {
            skip2 = std::max(skip1, skip2);
            skip1 += input;

        } else {
            skip2 += input;
            skip1 = std::max(skip0, skip1);
            skip0 += input;
        }
    }

    std::cout << std::max(skip1, (N % 2 == 0 ? skip0 : skip2)) << std::endl;

    return 0;
}
