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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

  public static void main(String[] args) throws Exception{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(br.readLine());
    String[] line = br.readLine().split(" ");
    long[] a = new long[n];
    for(int i = 0; i < n; i++){
      a[i] = Long.parseLong(line[i]);
    }
    int k = 1 + (n%2);
    long[][] dp = new long[n + 1][k + 2];
    for(int i = 0; i <= n; i++){
      Arrays.fill(dp[i], Long.MIN_VALUE);
    }
    dp[0][0] = 0;

    for(int i = 0; i < n; i++){
      for(int j = 0; j <= k; j++){
        dp[i + 1][j + 1] = Math.max(dp[i + 1][j + 1], dp[i][j]);
        long temp = dp[i][j];
        if((i + j) % 2 == 0 && i >= j) {
          temp += a[i];
        }
        dp[i + 1][j] = Math.max(dp[i + 1][j], temp);
      }
    }
    System.out.println(dp[n][k]);
  }
}
