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;
using ll = long long;
const int N = 200005;

int n, a[N];

ll dp[N][5];

ll f(int i, int left) {
	if(left < 0) return (ll)-1e18;
	if(i >= n) return left <= 1 ? 0 : (ll)-1e18;
	ll &ans = dp[i][left];
	if(~ans) return ans;
	ans = f(i + 1, left - 1);
	ans = max(ans, f(i + 2, left) + a[i]);
	return ans;
}

int main() {
	memset(dp, -1, sizeof dp);
	scanf("%d", &n);
	for(int i = 0; i < n; i++) scanf("%d", a + i);

	printf("%lld\n", f(0, n % 2 == 0 ? 1 : 2));
}
