Longest Consecutive

Have the function LongestConsecutive(arr) take the array of positive integers stored in arr and return the length of the longest consecutive subsequence (LCS). An LCS is a subset of the original list where the numbers are in sorted order, from lowest to highest, and are in a consecutive, increasing order. The sequence does not need to be contiguous and there can be several different subsequences. For example: if arr is [4, 3, 8, 1, 2, 6, 100, 9] then a few consecutive sequences are [1, 2, 3, 4], and [8, 9]. For this input, your program should return 4 because that is the length of the longest consecutive subsequence.

Examples

Input: [6, 7, 3, 1, 100, 102, 6, 12]
Output: 2

Input: [5, 6, 1, 2, 8, 9, 7]
Output: 5