Longest Consecutive Subsequence

Given an integer n and an array of n integers, your task is to find the length of the longest subsequence such that for every two consecutive elements a and b in the subsequence, the difference satisfies \( b - a = 1 \). Note that the subsequence can be obtained after sorting the array, and duplicate values are allowed; however, the difference between identical numbers is 0 and does not meet the condition.

Example:

• For the input array [1, 2, 3, 4, 5, 6], the longest subsequence is [1, 2, 3, 4, 5, 6] with length 6.
• For the input array [10, 12, 11, 14, 13], the longest subsequence is [10, 11, 12, 13, 14] with length 5.
• For the input array [20, 20, 20, 20], the longest subsequence is just [20] with length 1.

Use appropriate methods to read from stdin and write the answer to stdout.

inputFormat

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

outputFormat

Output a single integer representing the length of the longest subsequence where every two consecutive elements differ by exactly 1.

## sample

6
1 2 3 4 5 6

6

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