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#3972

Circular Barn 2s 512MB

Problems

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.


Input

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


Output

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


Example 

5
4
7
8
6
4
48

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


Source

USACO 2016 February Bronze

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