Open Olympiad in Design

Many people who prepare programming competitions used to be competitors themselves. This is good, because former competitors know the competition details and can write statements, run the judging system, and handle many other tasks. What would the competition look like if designers prepared it instead?

In an imaginary world, the Open Olympiad in Design takes place. There are $n$ problems. Each problem has its own statement designer, and there is one designer for problem names and one font designer. Each statement designer has already finished the work and left a fixed space for the problem name. The name of problem $i$ must have exactly $l_i$ characters.

Problem names must be made of Unicode characters, be distinct, and appear in lexicographical order. The font designer wants the names designer to satisfy all conditions while using as few distinct letters as possible. The order of the problems cannot be changed.

Find the minimum number of distinct letters needed to build $n$ words of the given lengths that are distinct and sorted in lexicographical order.

The first line contains a single integer $n$ ($1 \leq n \leq 100\,000$), the number of problems.

The second line contains $n$ integers $l_1, l_2, \ldots, l_n$ ($1 \leq l_i \leq 10^9$), the lengths of the problem names.

Print one integer, the minimum number of distinct letters the font designer has to paint.

A string $x_1 x_2 \ldots x_a$ is lexicographically smaller than a string $y_1 y_2 \ldots y_b$ if either the first position $i$ where they differ has $x_i < y_i$, or the first string is a strict prefix of the second string. A sequence of distinct words is sorted if each word is smaller than the next one.