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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

long max(long a, long b) {
  if (a >= b) {
    return a;
  } else {
    return b;
  }
}

int main(void) {

  long n;
  scanf("%ld", &n);
  long a[n];
  for (long i = 0; i < n; i++) {
    scanf("%ld", &a[i]);
  }
  long dp0[n/2][2],dp1[n/2][2];
  dp0[0][0] = 0;
  dp0[0][1] = a[0];
  dp1[0][0] = -10000000000;
  dp1[0][1] = a[1];
  for (long i = 1; i < n/2; i++) {
    dp0[i][0] = dp0[i-1][0]+a[i*2];
    dp0[i][0] = max(dp0[i][0],max(dp0[i-1][1],dp1[i-1][1]));
    dp0[i][1] = dp0[i-1][1]+a[i*2];
    dp1[i][0] = max(dp0[i-1][0],dp1[i-1][0])+a[i*2+1];
    dp1[i][1] = max(dp0[i-1][1],dp1[i-1][1])+a[i*2+1];
  }
  long ans;
  if (n%2 == 0) {
    ans = max(dp0[n/2-1][1],dp1[n/2-1][1]);
  } else {
    ans = dp0[n/2-1][0]+a[n-1];
    ans = max(ans,max(dp0[n/2-1][1],dp1[n/2-1][1]));
  }
  printf("%ld\n", ans);

  return 0;
}