CCO '16 P4 - O Canada

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 64M

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Problem type
Canadian Computing Olympiad: 2016 Day 2, Problem 1

In this problem, a grid is an N-by-N array of cells, where each cell is either red or white.

Some grids are similar to other grids. Grid A is similar to grid B if and only if A can be transformed into B by some sequence of changes. A change consists of selecting a 2-by-2 square in the grid and flipping the colour of every cell in the square. (Red cells in the square will become white; white cells in the square will become red.)

You are given G grids. Count the number of pairs of grids which are similar. (Formally, number the grids from 1 to G, then count the number of tuples (i, j) such that 1 \le i < j \le G and grid i is similar to grid j.)

Input Specification

The first line of input contains N (2 \le N \le 10), the size of the grids. The second line contains G (2 \le G \le 10\,000), the number of grids. The input then consists of N \cdot G lines, where each line contains N characters, where each character is either R or W, indicating the colour (red or white) for that element in the grid. Moreover, after the first two lines of input, the next N lines describe the first grid, the following N lines describe the second grid, and so on.

For 12 out of the 25 marks available for this question, 2 \le G \le 10.

Output Specification

Output the number of pairs of grids which are similar.

Sample Input

2
2
RW
WR
WR
RW

Sample Output

1

Explanation

There are exactly two grids, and they are similar because the first grid can be transformed into the second grid using one change (selecting the 2-by-2 square consisting of the entire grid).


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