Given a list of people with their birth and death years, implement a method to compute the year with the most number of people alive. You may assume that all people were born between 1900 and 2000 (inclusive). If a person was alive during any portion of that year, they should be included in that year's count. For example, Person (birth= 1908, death= 1909) is included in the counts for both 1908 and 1909.

If there are more than one years that have the most number of people alive, return the smallest one.

 

Example:


Input: 

birth = [1900, 1901, 1950]

death = [1948, 1951, 2000]

Output:  1901

 

Note: