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Gravity

There are several balls lying in the field. Every ball is pulled by gravity, but the direction of gravity is different for each ball!

You need to place a limited number of walls in the grid in such a way that every ball rolls into a different hole. The balls do not interact with each other, only with the walls. A ball starts rolling in the direction of the arrow in the ball. When it hits a wall, it will shift one row and column and continue rolling in the same direction. To be precise, a ball that hits a wall moves one square to the side and one square forward, so effectively it moves diagonally. If there is a hole in the square next to the wall, the ball will not roll into that hole. Walls cannot be placed on holes or arrows and a ball is not allowed to get stuck in a "basket" of two walls. Walls given in the puzzle count towards the total number of walls.

Example

In this puzzle there are three balls, one moving downwards, one moving to the right, and one moving upwards. The ball moving to the right rolls into a hole automatically (note that it doesn't interact with the arrow pointing up). The ball moving downwards should shift one column to the right. The only way to do this is by placing a wall directly below the arrow; if we would place the arrow in the bottom row, then it wouldn't fall into the hole. The ball moving up should also shift one column to the right. We cannot place the wall directly above the arrow, because this would block the ball moving down. Hence there is just one possible location for this wall.


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