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 <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
int n;
ll dp[200005], a[200005], b, ans = -1e15;
int main(){
	scanf("%d", &n);
	rep(i,n){
		scanf("%lld", a+i);
		dp[i] = (i>1?dp[i-2]:0) + a[i];
		if(i&1) dp[i] = max(dp[i], dp[i-1]);
	}
	if(n&1){
		for(int i=n-1; i>=0; i-=2){
			ans = max(ans, (i?dp[i-1]:0)+b);
			b += a[i];
		}
	}else ans = dp[n-1];
	printf("%lld\n", ans);
}
