Given an array of positive numbers, find the maximum sum of a subsequence with the constraint that no two numbers in the sequence should be adjacent in the array.

INPUT

First line contains two integers N denoting size of array

Next line contains N integers denoting elmenets of  array.

OUTPUT  

Output the maximum sum of array such that no two elements are adjacent.

CONSTRAINTS

$1 \leq N \leq 10^5$

$1 \leq A_i \leq 10^6$