A12187. The Fair Nut and Elevator
编程题
普及/提高-
知识点
题目描述
The Fair Nut lives in $n$ story house. $a_i$ people live on the $i$ -th floor of the house. Every person uses elevator twice a day: to get from the floor where he/she lives to the ground (first) floor and to get from the first floor to the floor where he/she lives, when he/she comes back home in the evening.
It was decided that elevator, when it is not used, will stay on the $x$ -th floor, but $x$ hasn't been chosen yet. When a person needs to get from floor $a$ to floor $b$ , elevator follows the simple algorithm:
- Moves from the $x$ -th floor (initially it stays on the $x$ -th floor) to the $a$ -th and takes the passenger.
- Moves from the $a$ -th floor to the $b$ -th floor and lets out the passenger (if $a$ equals $b$ , elevator just opens and closes the doors, but still comes to the floor from the $x$ -th floor).
- Moves from the $b$ -th floor back to the $x$ -th.
The elevator never transposes more than one person and always goes back to the floor $x$ before transposing a next passenger. The elevator spends one unit of electricity to move between neighboring floors. So moving from the $a$ -th floor to the $b$ -th floor requires $|a - b|$ units of electricity.Your task is to help Nut to find the minimum number of electricity units, that it would be enough for one day, by choosing an optimal the $x$ -th floor. Don't forget than elevator initially stays on the $x$ -th floor.
It was decided that elevator, when it is not used, will stay on the $x$ -th floor, but $x$ hasn't been chosen yet. When a person needs to get from floor $a$ to floor $b$ , elevator follows the simple algorithm:
- Moves from the $x$ -th floor (initially it stays on the $x$ -th floor) to the $a$ -th and takes the passenger.
- Moves from the $a$ -th floor to the $b$ -th floor and lets out the passenger (if $a$ equals $b$ , elevator just opens and closes the doors, but still comes to the floor from the $x$ -th floor).
- Moves from the $b$ -th floor back to the $x$ -th.
The elevator never transposes more than one person and always goes back to the floor $x$ before transposing a next passenger. The elevator spends one unit of electricity to move between neighboring floors. So moving from the $a$ -th floor to the $b$ -th floor requires $|a - b|$ units of electricity.Your task is to help Nut to find the minimum number of electricity units, that it would be enough for one day, by choosing an optimal the $x$ -th floor. Don't forget than elevator initially stays on the $x$ -th floor.
输入格式
The first line contains one integer $n$ ( $1 \leq n \leq 100$ ) — the number of floors.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \leq a_i \leq 100$ ) — the number of people on each floor.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \leq a_i \leq 100$ ) — the number of people on each floor.
输出格式
In a single line, print the answer to the problem — the minimum number of electricity units.
输入输出样例
输入 #1
3 0 2 1
输出 #1
16
输入 #2
2 1 1
输出 #2
4
说明/提示
In the first example, the answer can be achieved by choosing the second floor as the $x$ -th floor. Each person from the second floor (there are two of them) would spend $4$ units of electricity per day ( $2$ to get down and $2$ to get up), and one person from the third would spend $8$ units of electricity per day ( $4$ to get down and $4$ to get up). $4 \cdot 2 + 8 \cdot 1 = 16$ .
In the second example, the answer can be achieved by choosing the first floor as the $x$ -th floor.
In the second example, the answer can be achieved by choosing the first floor as the $x$ -th floor.