Longest consecutive run

Problem

A log holds event numbers in any order, possibly with repeats. A run is a group of numbers that follow each other, such as 4, 5, 6, 7.

Print the length of the longest run that can be made from the numbers in the log. Aim for O(n) time.

Input: One line of integers separated by spaces.
Output: One integer: the length of the longest run.
Constraints: 1 ≤ number of integers ≤ 100000
Integers are between -10⁹ and 10⁹

Example

Input

100 4 200 1 3 2

Output

The run 1, 2, 3, 4 has length 4.

Try the problem first. Open one hint at a time.

Hint 1

Put the numbers in a set. A number starts a run only when the number before it is not in the set.

Hint 2

From each start, count upward while the next number is in the set, and keep the largest count.

Write your Python code, run it on the examples and submit it to hidden tests.