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.

Examples

Input

6
1 2 3 4 5 6


Output

12


Input

5
-1000 -100 -10 0 10


Output

0


Input

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


Output

5000000000


Input

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


Output

295
#include <iostream>
using namespace std;
typedef long long ll;
ll dp[200001][3][2],n,a;
int main(void){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a;
        dp[i+1][0][1]=dp[i][0][0]+a;
        dp[i+1][1][1]=dp[i][1][0]+a;
        dp[i+1][2][1]=dp[i][2][0]+a;
        dp[i+1][0][0]=dp[i][0][1];
        dp[i+1][1][0]=max(dp[i][0][0],dp[i][1][1]);
        dp[i+1][2][0]=max(dp[i][1][0],dp[i][2][1]);
    }
    if(n%2==0)cout<<max(dp[n][0][0],dp[n][1][1]);
    if(n%2==1)cout<<max(dp[n][1][0],dp[n][2][1]);
}
