Is it possible to place (infinitely many) closed discs (of positive radius) in a unit square, where the interiors of the discs do not intersect, such that any point given in the interior of the square lies on a disc?

- The interior of each disc must be contained in the unit square. The perimeter of the disc can touch the perimeter of the square.
- The interiors of 2 discs do not intersect. The perimeters of the discs are allowed to intersect (so they touch each other).
- Note that the corners of the square cannot be covered by a closed disc, which is why I'm asking about the interior.

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