Gap

There are $N$ non-negative integers $a\_1, a\_2, \dots, a\_N$ satisfying the following inequality $0 \le a\_1 < a\_2 < \cdots < a\_N \le 10^{18}$. Jeehak wants to know the largest possible value of $a\_{i+1} - a\_i$ where $i$ ranges from $1$ to $N-1$. The input integers will not be given directly to Jeehak's program but will be accessible through a special funtion. See sections Implementation of your selected programming language for details.

Help Jeehak to implement a function to return the largest possible value of $a\_{i+1} - a\_i$ where $i$ ranges from $1$ to $N-1$.

In allsubtasks the constraint $2 \le N \le 100\\,000$ holds.