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: Wrong Answer)

import java.util.*;


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) {
            // even
            long sum1 = 0;
            long sum2 = 0;
            for (int i = 0; i < N; i++) {
                if (i%2 == 0) {
                    sum1 += A[i];
                } else {
                    sum2 += A[i];
                }
            }
            System.out.println(Math.max(sum1, sum2));
        } else {
            // odd
            long[] evenSum = new long[N];
            long[] oddSum = new long[N];
            for (int i = 0; i < N; i++) {
                if (i == 0) {
                    evenSum[0] = A[0];
                } else if (i == 1) {
                    oddSum[1] = A[1];
                } else if (i%2 == 0) {
                    evenSum[i] = evenSum[i-2]+A[i];
                } else {
                    oddSum[i] = oddSum[i-2]+A[i];
                }
            }
            long ans = Long.MIN_VALUE;
            for (int i = 1; i < N; i++) {
                long tmp = 0;
                if (i == 1) {
                    tmp = evenSum[N-1]-evenSum[0];
                } else if (i == N-1) {
                    tmp = evenSum[N-3];
                } else if (i%2 == 0) {
                    tmp += evenSum[i-2];
                    tmp += oddSum[N-2]-oddSum[i-1];
                } else {
                    tmp += oddSum[i-2];
                    tmp += evenSum[N-1]-evenSum[i-1];
                }
                ans = Math.max(tmp, ans);
            }
            System.out.println(Arrays.toString(evenSum));
            System.out.println(Arrays.toString(oddSum));
            System.out.println(ans);
        }
    }
}