E. Obtain a Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a rectangular matrix of size n \times m consisting of integers from 1 to 2 \cdot 10^5.In one move, you can:  choose any element of the matrix and change its value to any integer between 1 and n \cdot m, inclusive;  take any column and shift it one cell up cyclically (see the example of such cyclic shift below). A cyclic shift is an operation such that you choose some j (1 \le j \le m) and set a_{1, j} := a_{2, j}, a_{2, j} := a_{3, j}, \dots, a_{n, j} := a_{1, j} simultaneously.  Example of cyclic shift of the first column You want to perform the minimum number of moves to make this matrix look like this:  In other words, the goal is to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, \dots, a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, \dots, a_{n, m} = n \cdot m (i.e. a_{i, j} = (i - 1) \cdot m + j) with the minimum number of moves performed.InputThe first line of the input contains two integers n and m (1 \le n, m \le 2 \cdot 10^5, n \cdot m \le 2 \cdot 10^5) — the size of the matrix.The next n lines contain m integers each. The number at the line i and position j is a_{i, j} (1 \le a_{i, j} \le 2 \cdot 10^5).OutputPrint one integer — the minimum number of moves required to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, \dots, a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, \dots, a_{n, m} = n \cdot m (a_{i, j} = (i - 1)m + j).ExamplesInput
3 3
3 2 1
1 2 3
4 5 6
Output
6
Input
4 3
1 2 3
4 5 6
7 8 9
10 11 12
Output
0
Input
3 4
1 6 3 4
5 10 7 8
9 2 11 12
Output
2
NoteIn the first example, you can set a_{1, 1} := 7, a_{1, 2} := 8 and a_{1, 3} := 9 then shift the first, the second and the third columns cyclically, so the answer is 6. It can be shown that you cannot achieve a better answer.In the second example, the matrix is already good so the answer is 0.In the third example, it is enough to shift the second column cyclically twice to obtain a good matrix, so the answer is 2.
3 3
3 2 1
1 2 3
4 5 6

6 
['greedy', 'implementation', 'math', '*1900']