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 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class Main {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = sc.nextLong();
        }

        if(n % 2 == 0){
            long sumo = 0;
            long sume = 0;
            for (int i = 0; i < a.length; i++) {
                if(i % 2 == 0){
                    sume += a[i];
                }else{
                    sumo += a[i];
                }
            }
            System.out.println(Math.max(sume, sumo));
        }else{
            long[] sume = new long[n/2 + 2];
            long[] sumo = new long[n/2 + 2];
            for (int i = 0; i < a.length; i++) {
                if(i % 2 == 0){
                    sume[i/2 + 1] = sume[i/2] + a[i];
                }else{
                    sumo[i/2 + 1] = sumo[i/2] + a[i];
                }
            }
            sumo[n/2+1] = sumo[n/2];

            long ans = 0;
            for (int i = 0; i < n/2+1; i++) {
                long mans = sume[i] - sume[0];
                mans += sumo[n/2+1] - sumo[i+1];
                ans = Math.max(ans, mans);
            }
            for (int i = 0; i < n/2+1; i++) {
                long mans = sumo[i] - sumo[0];
                mans += sume[n/2+1] - sume[i+1];
                ans = Math.max(ans, mans);
            }

            System.out.println(ans);
        }
    }


    private static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private static boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

}