2016 AIME I Problem 14

Centered at each lattice point in the coordinate plane are a circle radius \frac{1}{10} and a square with sides of length \frac{1}{5} whose sides are parallel to the coordinate axes. The line segment from (0,0) to (1001, 429) intersects m of the squares and n of the circles. Find m + n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.