CF1765J.Hero to Zero

普及/提高-

通过率：0%

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题目描述

There are no heroes in this problem. I guess we should have named it "To Zero".

You are given two arrays $a$ and $b$ , each of these arrays contains $n$ non-negative integers.

Let $c$ be a matrix of size $n \times n$ such that $c_{i,j} = |a_i - b_j|$ for every $i \in [1, n]$ and every $j \in [1, n]$ .

Your goal is to transform the matrix $c$ so that it becomes the zero matrix, i. e. a matrix where every element is exactly $0$ . In order to do so, you may perform the following operations any number of times, in any order:

choose an integer $i$ , then decrease $c_{i,j}$ by $1$ for every $j \in [1, n]$ (i. e. decrease all elements in the $i$ -th row by $1$ ). In order to perform this operation, you pay $1$ coin;
choose an integer $j$ , then decrease $c_{i,j}$ by $1$ for every $i \in [1, n]$ (i. e. decrease all elements in the $j$ -th column by $1$ ). In order to perform this operation, you pay $1$ coin;
choose two integers $i$ and $j$ , then decrease $c_{i,j}$ by $1$ . In order to perform this operation, you pay $1$ coin;
choose an integer $i$ , then increase $c_{i,j}$ by $1$ for every $j \in [1, n]$ (i. e. increase all elements in the $i$ -th row by $1$ ). When you perform this operation, you receive $1$ coin;
choose an integer $j$ , then increase $c_{i,j}$ by $1$ for every $i \in [1, n]$ (i. e. increase all elements in the $j$ -th column by $1$ ). When you perform this operation, you receive $1$ coin.

You have to calculate the minimum number of coins required to transform the matrix $c$ into the zero matrix. Note that all elements of $c$ should be equal to $0$ simultaneously after the operations.

输入格式

The first line contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 10^8$ ).

The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ( $0 \le b_j \le 10^8$ ).

输出格式

Print one integer — the minimum number of coins required to transform the matrix $c$ into the zero matrix.

输入输出样例

输入#1
```
3
1 2 3
2 2 2
```
输出#1
```
2
```
输入#2
```
3
3 1 3
1 1 2
```
输出#2
```
5
```
输入#3
```
2
1 0
2 1
```
输出#3
```
2
```
输入#4
```
2
1 4
2 3
```
输出#4
```
4
```
输入#5
```
4
1 3 3 7
6 9 4 2
```
输出#5
```
29
```

说明/提示

In the first example, the matrix looks as follows:

111000111You can turn it into a zero matrix using $2$ coins as follows:

subtract $1$ from the first row, paying $1$ coin;
subtract $1$ from the third row, paying $1$ coin.

In the second example, the matrix looks as follows:

221001221You can turn it into a zero matrix using $5$ coins as follows:

subtract $1$ from the first row, paying $1$ coin;
subtract $1$ from the third row, paying $1$ coin;
subtract $1$ from the third row, paying $1$ coin;
subtract $1$ from $a_{2,3}$ , paying $1$ coin;
add $1$ to the third column, receiving $1$ coin;
subtract $1$ from the first row, paying $1$ coin;
subtract $1$ from $a_{2,3}$ , paying $1$ coin.

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