Problem Statement

There are $N$ people, Person $1$ through Person $N$, standing on a number line. Person $i$ is now at coordinate $A_i$ on the number line. Here, $A_1 < A_2 < A_3 < \dots < A_N$ and all $A_i$ are even numbers.

We will now hold a party for $k$ seconds. During the party, each person can freely move on the number line at a speed of at most $1$ per second. (It is also allowed to move in the negative direction within the speed limit.) The people request that the following condition be satisfied for every integer $i$ such that $1 \le i \lt N$:

• there is at least one moment during the party (including the moment it ends) when Person $i$ and Person $i + 1$ are at the same coordinate.

Find the minimum $k$ for which there is a strategy that the people can take to satisfy all the conditions. We can prove that the answer is an integer under the Constraints of this problem.

Constraints

• $2 \le N \le 2 \times 10^5$
• $0 \le A_i \le 10^9$
• $A_1 < A_2 < A_3 < \dots < A_N$
• $A_i$ is an even number.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 A_3 \dots A_N

Output

Print the answer as an integer.