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;


int main() {
	int n;
	cin >> n;
	long long a[201010];
	for (int i=0; i<n; i++) cin >> a[i+1];

	long long max_ch[201010], ht[201010];
	max_ch[1] = a[1];
	ht[1] = a[1];
	max_ch[2] = max(a[2], a[1]);
	max_ch[3] = max(max_ch[2], a[3]);
	ht[3] = a[1] + a[3];
	for (int i=4; i<=n; i++) {
		long long r1 = max_ch[i-2] + a[i];
		long long r2;
		if (i%2) r2 = max_ch[i-3] + a[i-1];
		else {
			r2 = ht[i-3] + a[i-1];
			ht[i-1] = r2;
		}
		max_ch[i] = max(r1, r2);
		//cout << i << ": " << max_ch[i] << " " << a[i] << endl;
	}

	cout << max_ch[n] << endl;
}
