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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  if(N%2==0){
    int64_t a=0;
    int64_t b=0;
    for(int i=0;i<N/2;i++){
      int64_t aa,bb;
      cin >> aa >> bb;
      a += aa;
      b += bb;
    }
    cout << max(a,b) << endl;
  }else{
    int64_t a=0;
    int64_t b=0;
    vector<int> in(N);
    for(int i=0; i<N;i++)
      cin >> in[i];
    int64_t m = 10000000001;
    for(int i=0;i<N/2;i++){
      int64_t aa = in[2*i];
      int64_t bb = in[2*i+1];
      m = min(m, aa);
      a += aa;
      b += bb;
    }
    int64_t aa;
    aa = in[N-1];
    m = min(m, aa);
    a += aa;
    int64_t ans = max(a-m, b);
    for(int i=0; i<N/2; i++){
      int64_t aaa = a;
      aaa -= in[2*i] + in[2*i+2];
      aaa += in[2*i+1];
      ans = max(ans, aaa);
    }
    cout << ans << endl;
  }
}