CF500C New Year Book Reading

New Year is coming, and Jaehyun decided to read many books during 2015, unlike this year. He has $ n $ books numbered by integers from 1 to $ n $ . The weight of the $ i $ -th ( $ 1

The first line contains two space-separated integers $ n $ ( $ 2

Print the minimum total weight of books he should lift, which can be achieved by rearranging the order of stacked books.

Here's a picture depicting the example. Each vertical column presents the stacked books.