A. Weird Sumtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputEgor has a table of size n \times m, with lines numbered from 1 to n and columns numbered from 1 to m. Each cell has a color that can be presented as an integer from 1 to 10^5.Let us denote the cell that lies in the intersection of the r-th row and the c-th column as (r, c). We define the manhattan distance between two cells (r_1, c_1) and (r_2, c_2) as the length of a shortest path between them where each consecutive cells in the path must have a common side. The path can go through cells of any color. For example, in the table 3 \times 4 the manhattan distance between (1, 2) and (3, 3) is 3, one of the shortest paths is the following: (1, 2) \to (2, 2) \to (2, 3) \to (3, 3). Egor decided to calculate the sum of manhattan distances between each pair of cells of the same color. Help him to calculate this sum.InputThe first line contains two integers n and m (1 \leq n \le m, n \cdot m \leq 100\,000) — number of rows and columns in the table.Each of next n lines describes a row of the table. The i-th line contains m integers c_{i1}, c_{i2}, \ldots, c_{im} (1 \le c_{ij} \le 100\,000) — colors of cells in the i-th row.OutputPrint one integer — the the sum of manhattan distances between each pair of cells of the same color.ExamplesInput
2 3
1 2 3
3 2 1
Output
7
Input
3 4
1 1 2 2
2 1 1 2
2 2 1 1
Output
76
Input
4 4
1 1 2 3
2 1 1 2
3 1 2 1
1 1 2 1
Output
129
NoteIn the first sample there are three pairs of cells of same color: in cells (1, 1) and (2, 3), in cells (1, 2) and (2, 2), in cells (1, 3) and (2, 1). The manhattan distances between them are 3, 1 and 3, the sum is 7.
2 3
1 2 3
3 2 1

7 
['combinatorics', 'data structures', 'geometry', 'math', 'matrices', 'sortings', '*1400']