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;

typedef long long	ll;

const int N = int(2e5) + 10;
bool vis[N][2][3];
ll dp[N][2][3];
ll pref[2];
ll suf[2];
ll a[N];
const ll inf = ll(1e18);
int n;

ll solve(int i, int flag, int cnt){
	if(cnt > 2){
		return -inf;
	}

	if(i == n){
		return cnt >= 1 ? 0 : -inf;
	}

	bool &v = vis[i][flag][cnt];
	ll &ans = dp[i][flag][cnt];

	if(v){
		return ans;
	}

	v = true;

	ans = -inf;

	if(flag){
		ans = solve(i + 1, 0, cnt) + a[i];
	}

	ans = max(ans, solve(i + 1, 1, cnt + flag));

	return ans;
}

int main(){
	scanf("%d", &n);

	for(int i = 0 ; i < n ; i++){
		scanf("%lld", &a[i]);
	}

	if(n & 1){
		printf("%lld\n", solve(0, 1, 0));
	}else{
		for(int i = 0 ; i < n ; i++){
			pref[i & 1] += a[i];
		}

		printf("%lld\n", max(pref[0], pref[1]));
	}

	return 0;
}