Lexicographic constraints

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

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

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

样例

3
3 2 1

2