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.util.Scanner;

public class Main {

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N =sc.nextInt();
		int a[] = new int[N+1];
		for (int i=0;i<N;i++) {
			a[i] =sc.nextInt();
		}
		long sum =0;
		long dp0[]= new long[N+1];
		long dp1[]= new long[N+1];
		long dp2[]= new long[N+1];
		dp0[0] = 0;
		dp1[0] = a[0];
		dp0[1] = 0;
		dp1[1] = Math.max(a[0], a[1]);
		dp2[1] = Math.max(a[0], a[1]);
		dp0[2] = 0;
		dp1[2] = Math.max(a[0], Math.max(a[1], a[2]));
		dp2[2] = a[0]+a[2];
		for (int i=3;i<N;i++) {
			if (i%2==0) {
				dp0[i] = Math.max(dp0[i-2]+a[i], dp1[i-2]);
				dp0[i] = Math.max(dp0[i], dp0[i-1]);
				dp1[i] = Math.max(dp1[i-2]+a[i], dp2[i-2]);
				dp1[i] = Math.max(dp1[i], dp1[i-1]);
				dp2[i] = dp2[i-2]+a[i];
			} else {
				dp0[i] = Math.max(dp0[i-2]+a[i],dp1[i-2]);
				dp0[i] = Math.max(dp0[i], dp1[i-1]);
				dp1[i] = Math.max(dp1[i-2]+a[i],dp2[i-1]);
				dp2[i] = dp1[i];
			}
		}
		if (N%2==1) {
			System.out.println(Math.max(dp1[N-1], dp1[N-2]));
		} else {
			System.out.println(Math.max(dp1[N-1], dp2[N-2]));
		}
	}
}