## Snow Removal

Points: 5
Time limit: 2.0s
Memory limit: 256M

Author:
Problem type

The entrance to CB is blocked with snow! The snow can be represented as an array of $$N$$ integers, where the $$i$$-th integer is the amount of snow in the $$i$$-th area ($$1 \le i \le N$$).

You are tasked with moving the snow.

It takes exactly $$1$$ minute for you to move $$1$$ unit of snow from one area to the one of the neighbouring areas.

Formally, moving $$1$$ unit of snow from the $$i$$-th area ($$1 \le i \le N$$) to the $$i-1$$-th area or to the $$i+1$$-th area takes 1 minute.

Your goal is to move all the snow so that each unit of snow is either located in the $$0$$-th area or the $$N+1$$-th area.

#### Constraints

$$1 \le N \le 10^5$$

$$1 \le A_i \le 10^9$$

#### Input Specification

The first line contains an integers $$N$$, which is the number of areas.

The next line contains $$N$$ space-separated integers, $$A_i$$, the amount of snow in the $$i$$-th area.

#### Output Specification

Output the minimum amount of time needed to time to move all the snow.

#### Sample Input 1

5
3 1 4 1 5

#### Sample Output 1

24