Obstacle Course

Morgan is a businessman and parkour enthusiast who owns an obstacle course of $N$ road segments, numbered from $1$ to $N$. Segment $1$ is adjacent to segment $2$, segment $2$ is adjacent to segment $3$, and so on, up to segment $N-1$ adjacent to segment $N$. Each odd-numbered segment has a positive integer height $A_i$, and each even-numbered segment has height $0$. On Morgan's course, anyone can start from any segment, move in one direction, and stop at any segment they can reach.

Adrian is a beginner. He keeps going while the height difference between the current segment and the next one is exactly $1$. If the difference is more than $1$, he cannot climb up or jump down, so he stops. If the next segment has the same height as the current one, he loses interest and stops. He also stops when he reaches segment $N$ or segment $1$, the end of the course. Adrian's happiness is the number of segments he passes before he stops. He starts from whichever segment gives him the largest happiness.

Morgan wants Adrian to enjoy the course, so he changes the heights of some even-numbered segments (possibly none) to maximize Adrian's largest happiness. Find the largest happiness Adrian can have after the changes.

For example, let $A_{1..9} = [6, 0, 4, 0, 8, 0, 12, 0, 14]$. If $A$ is changed to $[6, 5, 4, 5, 8, 11, 12, 13, 14]$, Adrian can go from segment 1 to 4, or from segment 6 to 9, and his happiness is 4, which is the largest after the change. Other changes also reach 4, such as $[6, 5, 4, 3, 8, 7, 12, 12, 14]$, but no change can make the value larger than 4.

The first line contains an integer $N$ ($2 \le N \le 100000$). The second line contains $N$ integers $A_i$. $A_i = 0$ if $i$ is even, and $1 \le A_i \le 100000$ if $i$ is odd.

Print one integer on a single line: the largest possible happiness of Adrian on Morgan's new course.