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>
#define all(x) begin(x), end(x)
#define _ << ' ' <<
using namespace std;
using ll = long long;

ll a[200000];
ll dp[200000][3];
int n;

ll f(int i, int s)
{
    if (i >= n)
        return 0;
    ll& sol = dp[i][s];
    if (sol != -1)
        return sol;
    sol = a[i] + f(i + 2, s);
    if (s > 0)
        sol = max(sol, f(i + 1, s - 1));
    return sol;
}

int main()
{
    cin >> n;
    for (int i = 0; i < n; ++i)
        cin >> a[i];
    memset(dp, -1, sizeof dp);
    cout << f(0, n % 2 + 1);
}
