Weird Sum

题意翻译

### 题意简述： 给出两个整数 $n,m ( 1 \leq n \le m, n \cdot m \leq 100000) $，和一个 $n \times m$ 的矩阵。若该矩阵中两元素相同，$sum$(初始为零)就加上它们所在位置的曼哈顿距离。求 $sum$ 的值。

题目描述

Egor 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.

输入输出格式

输入格式

The 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.

输出格式

Print one integer — the the sum of manhattan distances between each pair of cells of the same color.

输入输出样例

输入样例 #1

2 3
1 2 3
3 2 1

输出样例 #1

7

输入样例 #2

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

输出样例 #2

76

输入样例 #3

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

输出样例 #3

129

说明

In 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 $ .