LogiQuest

266. Max Sum without Three Consecutive

MediumDynamic Programming

Pick elements so that no three consecutive elements are all picked. Print the maximum sum of picked elements (values are non-negative).

Input format

Line 1: n Line 2: n non-negative integers

Output format

The maximum sum.

Example 1

Input

5
3000 2000 1000 3 10

Output

5013

Example 2

Input

3
1 2 3

Output

5

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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