Kamina is interested in brotherly sequences. A **brotherly sequence** is a sequence where for every index , and . Given a sequence of numbers of length , what is the length of the longest **contiguous brotherly subsequence** it contains?

#### Input Specification

The first line of input will contain the integer .

The second line of input will contain space-separated integers making up the sequence . The numbers in are in the range .

#### Output Specification

The positive integer length of the longest brotherly subsequence in the sequence .

#### Sample Input

```
5
1 1 2 4 8
```

#### Sample Output

`4`

#### Note

A *subsequence* of a sequence is a sequence that is formed by deleting some elements of the original sequence, but preserving the relative order of the remaining elements. A *contiguous* subsequence is a subsequence formed by deleting some prefix and some suffix of the sequence (possibly empty for either or both).

## Comments

Hello! :D This is a hard question if you ask me. :(

Shouldnt it be contest 5?

No, because Exam Time was the fourth contest of the 2014 DMOPCs. The URL for the Exam Time problems had "ce" instead of "c4" though, so I guess that's why the URL for all the 2014 DMOPCs after Exam Time were 1 off.

Can we have another input/output sample?

No, we believe the existing sample is enough.

Can there be an explanation for the sample output? Such as what the longest contiguous brotherly subsequence would be?

For the sample input, we can remove the last element of the sequence. The resulting subsequence is maximal.