Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

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

Sample Output 4

295

Solution in Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];
        for(int i=0;i<N;i++){
            a[i] = sc.nextInt();
        }
        if(N%2==0){
            long ans = 0;
            long leftSum = 0, rightSum = 0;
            for(int i=0;i<N/2+1;i++){
                leftSum = 0;
                rightSum = 0;
                for(int x=0;x<i;x++) {
                    leftSum += a[x * 2];
                }
                for(int y=i;y<N/2;y++){
                    rightSum += a[y * 2 + 1];
                }
                if(leftSum + rightSum > ans){
                    ans = leftSum + rightSum;
                }
            }
            System.out.println(ans);
        }else{
            long ans = 0;
            long leftSum = 0, rightSum = 0, centerSum = 0;
            for(int i=0;i<N/2+1;i++){
                leftSum = 0;
                for (int x = 0; x < i; x++) {
                    leftSum += a[x * 2];
                }
                for(int j=i; j<N/2+1;j++) {
                    rightSum = 0;
                    centerSum = 0;
                    for (int y = j; y < N / 2; y++) {
                        rightSum += a[y * 2 + 2];
                    }
                    for (int z = i; z < j; z++){
                        centerSum += a[z * 2 + 1];
                    }
                    if (leftSum + rightSum + centerSum > ans) {
                        ans = leftSum + rightSum + centerSum;
                    }
                }
            }

            System.out.println(ans);
        }
    }
}