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
import sys
n=int(input())
a=list(map(int,input().split()))


if n==2:
    print(max(a))
    sys.exit()

a0=[a[0],a[0]]
a1=[0,a[1]]
a2=[0,0,a[2]]
for i in range(2,n):
    if i%2==0:
        a0.append(a0[i-2]+a[i])
        a1.append(a1[i-1])
        if i>=4: a2.append(max(a2[i-2],a1[i-3],a0[i-4])+a[i])
    else:
        a0.append(a0[i-1])
        a1.append(max(a1[i-2],a0[i-3])+a[i])
        a2.append(a2[i-1])

if n%2==1: print(max(a0[n-1],a1[n-1],a2[n-1]))
else: print(max(a0[n-1],a1[n-1]))