Arranging Seats

There are n students sitting at desks arranged in a line, and each student has a score. A seating arrangement is valid if it can be obtained by sorting the scores in nondecreasing order and then rotating that sorted array. Students with the same score only need to be adjacent, and their relative order does not matter.

For example, for the score array {10 20 20 30}, all of {10 20 20 30}, {20 20 30 10}, {20 30 10 20}, and {30 10 20 20} are valid seating arrangements. However, {30 20 20 10} is not valid because it is not a rotation of the nondecreasing array.

The grading results arrived late, after all students had gone to sleep, so the assistant must move the students' computers to prepare the next day's seating arrangement.

The assistant has only two arms, so at most two computers can be carried at once. Moving one position while carrying computers costs force equal to the number of computers being carried. Also, lifting one computer from a desk costs 10 force, and placing one computer on a desk costs 10 force.

Given the scores in the current seating order, compute the minimum force needed to make a valid seating arrangement.

The first line contains the number of students n. (2 <= n <= 400)

The second line contains the students' scores in their current seating order. Each score is a positive integer not exceeding 2,000,000.

Print the minimum force needed to make a valid seating arrangement.