Problem Statement

We have a sequence of $N$ terms: $a_1,a_2,\ldots,a_N$. You can perform the following operation on this sequence any number of times (possibly zero).

• Choose a term of the sequence at that point, and let $s$ be its value. Then, for every $1\leq i\leq N$, replace $a_i$ with $2s-a_i$. However, this operation may not be performed in a way that produces a term with a negative value.

You want to make the greatest value among the terms of the sequence as small as possible. What will this value be after an optimal sequence of operations for this objective?

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq a_1 < a_2 < \ldots < a_N \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

Print the answer.