Circle and Points

Input

The input consists of several data sets. The end of input is indicated by a line containing a single $0$.

Each data set starts with a line containing a single integer $N$ (1 \le N \le 300), the number of points.

Next follow $N$ lines, each containing two decimal numbers $X$ and $Y$ (0.0 \le X, Y \le 10.0), the coordinates of a point. Coordinates are given with $5$ digits after the decimal point.

No two points are closer than $0.0001$ to each other. No two points within a data set are at approximately distance $2.0$ from each other, that is, the distance $d$ between any pair of points never satisfies 1.9999 \le d \le 2.0001.

Furthermore, no three points within a data set are simultaneously very close to being co-circular with a unit circle. Specifically, for any three distinct points P_1, P_2, P_3 in a data set, and for any arbitrary point in the plane, let d_1, d_2, d_3 be the distances from that point to P_1, P_2, and P_3, respectively. Then it never simultaneously holds that 0.9999 \le d_i \le 1.0001 for i = 1,2,3.

Output

For each data set, print the maximum number of points that can simultaneously be inside or on a unit circle, one per line.

Examples