J. Hero to Zerotime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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).OutputPrint one integer — the minimum number of coins required to transform the matrix c into the zero matrix.ExamplesInput
3
1 2 3
2 2 2
Output
2
Input
3
3 1 3
1 1 2
Output
5
Input
2
1 0
2 1
Output
2
Input
2
1 4
2 3
Output
4
Input
4
1 3 3 7
6 9 4 2
Output
29
NoteIn the first example, the matrix looks as follows: 111000111 You 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: 221001221 You 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. 
3
1 2 3
2 2 2

2 
['graph matchings', 'math', '*2900']