Farmer George has a chicken farm. The chickens live in a hen house. There are N nesting-boxes where the chickens lay their eggs. These nesting-boxes are numbered from 1 to N consecutively. The K^th nesting-box is neighboring with K-1^th and K+1^th nesting-boxes.

The chickens lay their eggs in any of the nesting-boxes. Thus, each morning there can be different numbers of eggs in the boxes, and some boxes can be empty.

Farmer George uses a robot to collect the eggs in the nesting-boxes. The robot collects the eggs every morning and it has been programmed as follows:

• It enters a box only once and picks all the eggs there.
• When it takes the eggs from a box, it takes the eggs from two neigbouring nesting-boxes.
• When the eggs from two consecutive boxes have been taken, the next one must be skipped.
• It can skip as many boxes as it wishes.

Question:
To help farmer George, write a program that calculates the maximum number of eggs that can be gathered by the robot.

Input specification
The first line of the input has an integer N (2 ≤ N ≤ 2500) representing the number of the nesting-boxes. In the second line, there are N integers (each in the 0..100 range) representing number of the eggs in the nesting-boxes. The first number is for the first nesting-box, the second one is for the second nesting-box, and so on. The numbers in the second line are separated by a space.

Output specification
Show just one integer number: maximum number of eggs that can be gathered by the robot.

Explanation: (3+4) + (6+7) + (2+1) = 23

Time Limit: 0.1 second /test.