Score : $700$ points

Problem Statement

There are $N$ strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, $S_1 holds lexicographically, where$S_i$is the$i$-th string from the left.

At least how many different characters are contained in $S_1,S_2,...,S_N$, if the length of $S_i$ is known to be $A_i$?

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq A_i \leq 10^9$
• $A_i$ is an integer.

Note

The strings do not necessarily consist of English alphabet; there can be arbitrarily many different characters (and the lexicographic order is defined for those characters).

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

Output

Print the minimum possible number of different characters contained in the strings.

3
3 2 1

2

The number of different characters contained in $S_1,S_2,...,S_N$ would be $3$ when, for example, $S_1=$abc, $S_2=$bb and $S_3=$c.

However, if we choose the strings properly, the number of different characters can be $2$.

5
2 3 2 1 2

2