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<S_2<...<S_N 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?

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.

Constraints

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

Sample Input 1

3
3 2 1

Sample Output 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.

Sample Input 2

5
2 3 2 1 2

Sample Output 2

2

见题面 Input 部分

见题面 Output 部分