Statement

John is playing the new hit mobile game: "The Jeweller's Game". In this game, there is an N × N board full of different kinds of gems. Let's denote by (r, c) the cell located at the r-th row and c-th column of the board. Each cell of the board contains a gem. The type of the gem in cell (r,c) is represented by a positive integer G_r,c. We group the cells according to the following rule. Cells a and b are in the same group if and only if there exists a sequence of cells p_0, …, p_k such that: (1) p_0 = a and p_k = b, and (2) cells p_i-1 and p_i are edge-adjacent and are of the same type for each i = 1, …, k. Note that every cell belongs to exactly one group. The player can improve their score by swapping edge-adjacent cells of the board. Depending on whether the two swapped cells are in the same row or in the same column, we call a swap either horizontal or vertical, respectively. If the two swapped gems are of the same type, then the score of the swap is 0...