Problem Description

Xiao C and the grid are good friends.

Xiao C has a grid with $n$ rows and $m$ columns. Each cell contains a number, and the number in the cell at row $i$ and column $j$ is $a_{i,j}$.

We define that, in this grid, two different cells are non-adjacent if and only if these two cells do not share a common edge.

Xiao C thinks that two different cells are good friends of each other if and only if these two cells are non-adjacent and the numbers in these two cells are the same.

Xiao C wants you to help compute the total sum of the number of good friends over all cells.

Input Format

The first line contains two integers $n,m$.

The next $n$ lines each contain $m$ integers, where the $j$-th integer in the $i$-th line represents $a_{i,j}$.

Output Format

Output one integer, representing the total sum of the number of good friends over all cells.

3 4
1 1 4 5
2 1 2 3
3 1 4 1

20

Hint

Sample Explanation #1

The cell in row $1$ column $1$ has $3$ good friends, the cell in row $1$ column $2$ has $2$ good friends, the cell in row $1$ column $3$ has $1$ good friend, and the cell in row $1$ column $4$ has $0$ good friends.

The cell in row $2$ column $1$ has $1$ good friend, the cell in row $2$ column $2$ has $2$ good friends, the cell in row $2$ column $3$ has $1$ good friend, and the cell in row $2$ column $4$ has $1$ good friend.

The cell in row $3$ column $1$ has $1$ good friend, the cell in row $3$ column $2$ has $3$ good friends, the cell in row $3$ column $3$ has $1$ good friend, and the cell in row $3$ column $4$ has $4$ good friends.

The total sum of the number of good friends over all cells is $20$.

Sample #2

See square/square2.in and square/square2.ans in the additional files.

This sample satisfies the constraints of test point $1$.

Sample #3

See square/square3.in and square/square3.ans in the additional files.

This sample satisfies the constraints of test point $4$.

Sample #4

See square/square4.in and square/square4.ans in the additional files.

This sample satisfies the constraints of test point $6$.

Sample #5

See square/square5.in and square/square5.ans in the additional files.

This sample satisfies the constraints of test point $10$.

Constraints

For $100\%$ of the testdata, $1 \le n,m \le 2000$, and $1 \le a_{i,j} \le 9$.

Special property: It is guaranteed that the numbers in any two adjacent cells are different.

Translated by ChatGPT 5