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.</p>

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 형식

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

출력 형식

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

예제 입력

5
4
7
8
6
4

예제 출력

48

힌트

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