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 int long long
const int N = 2e5 + 5,INF = 0xfeeddeadbeef,inf = INF >> 1;
int n,a[N];
map<int,int> dp[N];
int DP(int i,int k) {
	if(k > (i+1>>1)) return -inf;
	if(i <= 0) return 0;
	if(dp[i][k]) return dp[i][k];
	return dp[i][k] = max(DP(i-2,k-1) + a[i],DP(i-1,k));
}
signed main() {
	cin >> n;
	for(int i = 1;i <= n;++i)	
		cin >> a[i];
	cout << DP(n,n>>1) << endl;
	return 0;
}
