시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 512 MB99851046451.327%

## 문제

Being a fan of contemporary architecture, Farmer John has built a new barn in the shape of a perfect circle. Inside, the barn consists of a ring of $$n$$ rooms, numbered clockwise from $$1 \ldots n$$ around the perimeter of the barn ($$3 \leq n \leq 1,000$$). Each room has doors to its two neighboring rooms, and also a door opening to the exterior of the barn.

Farmer John wants exactly $$r_i$$ cows to end up in each room $$i$$ ($$1 \leq r_i \leq 100$$). To herd the cows into the barn in an orderly fashion, he plans to unlock the exterior door of a single room, allowing the cows to enter through that door. Each cow then walks clockwise through the rooms until she reaches a suitable destination. Farmer John wants to unlock the exterior door that will cause his cows to collectively walk a minimum total amount of distance. Please determine the minimum total distance his cows will need to walk, if he chooses the best such door to unlock. The distance walked by a single cow is the number of interior doors through which she passes.

## 입력

The first line of input contains $$n$$. Each of the remaining $$n$$ lines contain $$r_1 \ldots r_n$$.

## 출력

Please write out the minimum total amount of distance the cows collectively need to travel.

5
4
7
8
6
4

48

## 힌트

In this example, the best solution is to let the cows enter through the door of the room that requires 7 cows.