Origami Probability

Geometry Level 4

A square sheet of paper has its center marked with point OO. A random point is uniformly chosen on the square paper, and this point is labeled PP. The paper is then folded so that point PP coincides with point OO. Let the probability that a pentagon is formed after the fold be NN. Find the value of 1000N\lfloor 1000N \rfloor.

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