Longest Consecutive Sequence

You are given a list of integers and your task is to find the length of the longest consecutive sequence in the list. A consecutive sequence is a set of numbers that follow each other without interruption. For example, in the list [100, 4, 200, 1, 3, 2], the longest consecutive sequence is [1, 2, 3, 4] which has a length of 4.

The sequence is defined formally as follows: if \(a, a+1, a+2, \ldots, a+k\) are all present in the list, then the length of this sequence is \(k+1\). If the list is empty, the answer is 0.

Your program should read input from standard input and write the result to standard output.

inputFormat

The first line of input contains a single integer \(n\) which denotes the number of elements in the list. The second line contains \(n\) space-separated integers representing the list.

If \(n = 0\), the second line may be empty.

outputFormat

Output a single integer representing the length of the longest consecutive sequence.

## sample

6
100 4 200 1 3 2

4

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