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;

typedef long long ll;

const int N = 200200;
const ll Inf = 1e18;

int n;
int a[N];
ll Dp[N][3];

ll Rec(int i, int j)
{
    if(j < 0)   return -Inf;
    if(i >= n)  return j <= 1 ? 0 : -Inf;

    if(Dp[i][j] + 1)    return Dp[i][j];

    return Dp[i][j] = max(a[i] + Rec(i + 2, j), Rec(i + 1, j - 1));
}

int main()
{
    cin >> n;

    for(int i = 0; i < n; i++)  scanf("%d", a + i);

    memset(Dp, -1, sizeof(Dp));

    cout << Rec(0, n & 1 ? 2 : 1) << endl;
}
