Longest Consecutive Subsequence

You are given an array of integers. Your task is to determine the length of the longest subsequence of consecutive integers present in the array. A subsequence of consecutive integers means that if an integer x is in the subsequence, then x+1 should also appear, and so on. Note that the consecutive numbers do not need to appear in order in the original array.

For example, given the input array [100, 4, 200, 1, 3, 2], the longest consecutive subsequence is [1, 2, 3, 4] with a length of 4.

Note: In this problem, the input is provided via stdin and the output is expected on stdout.

The mathematical description of the consecutive property can be stated as follows: For a set \( S \) of integers, for any \( x \in S \), if \( x - 1 \notin S \), then starting from \( x \) the length of the consecutive sequence is given by finding the maximum \( k \) such that \( \{ x, x+1, \ldots, x+k-1 \} \subseteq S \). The answer is the maximum \( k \) over all such starting points.

inputFormat

The first line of the input contains an integer \( n \) indicating the number of elements in the array. The second line contains \( n \) space-separated integers representing the elements of the array.

Example:

6
100 4 200 1 3 2

outputFormat

Output a single integer, which is the length of the longest consecutive subsequence in the array.

Example:

4

## sample

6
100 4 200 1 3 2

4