Longest Consecutive Subsequence

Given an array of n integers, your task is to find the length of the longest subsequence (not necessarily contiguous in the original order) such that the elements can be rearranged to form a sequence of consecutive integers. Formally, you need to find the maximum length k for which there exists a set of integers {a, a+1, ..., a+k-1} that can be obtained by reordering a subset of the given array.

For example, consider the array [10, 3, 5, 1, 4, 2]. The longest such subsequence is [3, 5, 1, 4, 2] which can be rearranged to form [1, 2, 3, 4, 5] and has a length of 5.

Note: If there are no elements, the answer is 0.

inputFormat

The input is given via standard input (stdin). The first line contains an integer $n$, indicating the number of elements in the array. The second line contains $n$ space-separated integers representing the array elements.

outputFormat

Output a single integer representing the length of the longest subsequence that can be rearranged to form a sequence of consecutive integers. The answer should be printed to standard output (stdout).## sample

6
10 3 5 1 4 2

5