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.

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.

Examples

Input

3
3 2 1

Output

2

Input

5
2 3 2 1 2

Output

2

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