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, S1​<S2​<...<SN​ holds lexicographically, where Si​ is the $i$-th string from the left.

At least how many different characters are contained in S1​,S2​,...,SN​, if the length of Si​ is known to be Ai​?

Constraints

• 1≤N≤2×105
• 1≤Ai​≤109
• Ai​ 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).

Sample Input 1

3
3 2 1

Sample Output 1

2

The number of different characters contained in S1​,S2​,...,SN​ would be $3$ when, for example, S1​=abc, S2​=bb and S3​=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