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?

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).

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