Statement

The organizing committee of an unspecified programming contest (UPC) is planning to hold many rounds this year, each round consisting of N problems of varying difficulties. The problems in a round are numbered from 1 to N. As such, there have been a lot of problem proposals. Each problem proposal has a difficulty rating, which is either (1) an integer i (1 < i < N) -- meaning that this problem is appropriate as problem i in a round; or (2) a value in the form i.5 for some integer i (1 < i < N) -- meaning that this problem is appropriate as either problem i or problem i+1 in a round. Given the value of N and the number of problem proposals for each difficulty rating, find the maximum number of rounds that can be created using these problems. Each problem can only be used in at most one round.