Obtain a Permutation

You are given a rectangular matrix of size n × m consisting of integers from 1 to 2 ⋅ 10^5.

In one move, you can:

• choose any element of the matrix and change its value to any integer between 1 and n ⋅ 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 ≤ j ≤ m) and set a_{1, j} := a_{2, j}, a_{2, j} := a_{3, j}, ..., 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, ..., a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, ..., a_{n, m} = n ⋅ m (i.e. a_{i, j} = (i - 1) ⋅ m + j) with the minimum number of moves performed.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5, n ⋅ m ≤ 2 ⋅ 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 ≤ a_{i, j} ≤ 2 ⋅ 10^5).

Output

Print one integer — the minimum number of moves required to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, ..., a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, ..., a_{n, m} = n ⋅ m (a_{i, j} = (i - 1)m + j).

Examples

Input

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

Note

In 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.

inputFormat

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5, n ⋅ m ≤ 2 ⋅ 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 ≤ a_{i, j} ≤ 2 ⋅ 10^5).

outputFormat

Output

Print one integer — the minimum number of moves required to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, ..., a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, ..., a_{n, m} = n ⋅ m (a_{i, j} = (i - 1)m + j).

Examples

Input

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

Note

In 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.

样例

3 3
3 2 1
1 2 3
4 5 6

6

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