Any optimal circle of radius r can be shifted so at least 2 points lie on its boundary (unless answer = 1). Fix one point as anchor on circumference.

For anchor A and another point B within distance 2r, compute the center angle arc where both A and B remain inside the circle. Collect all [start, end) angle intervals, sort, and angular sweep for max overlap.

Handle floating precision with epsilon (1e-9). If all points fit in one circle (early exit check), answer = n. For duplicate points, treat them as one at same angle.