There is a long east-west road which has  towns situated along it, numbered  to  from west to east. All towns buy and sell the same kind of goodie. The value of a goodie fluctuates according to a weekly schedule. A town buys and sells a goodie at its value in that town on that particular day. At town , the value of a goodie changes by  every day in the first half of a week, and changes by  every day in the second half of a week. In other words, the value of a goodie at town  is  on Mondays and Sundays,  +  on Tuesdays and Saturdays,   on Wednesdays and Fridays, and  on Thursdays.

A merchant is making a business travel plan. His trip begins at a starting town  and ends at a destination town , visiting each town from  to  (inclusive) exactly once. The merchant starts the trip on a Monday. It takes him exactly one day to travel between adjacent towns and every day he travels to the next town on the path to the destination. He may buy exactly one goodie at a town along the trip and sell that goodie at a town he visits later. He can only buy once and sell once. The merchant would like to know the maximum possible profit of  travel plans with different choices of town  and town .