1 2 3 4 5

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1 | 0 0 0 0 0

2 | 0 0 1 0 0

3 | 0 0 0 0 0

4 | 1 0 0 0 0

5 | 0 0 0 0 0

with two points: (x1, y1) = (2, 3) and (x2, y2) = (4, 1).

The fastest way to find out whether these two points share the same diagonal is the result of this expression:

**bool result = (x1 + y1 == x2 + y2) or (x1 - y1 == x2 - y2)**

Now let's complicate the task. Given matrix n x n with m points, find the minimum number of diagonals which contain at least two points. The first line of the input contains: n m. The next m lines contain points with coordinates (xi, yi).