Lazy Fox

Your pet fox loves treats. There are N neighbors at distinct points on the plane, each with unlimited treats. The fox starts at the origin, which is not one of the neighbor points.

The fox visits locations to collect one treat per visit. It may revisit earlier locations, but never the same location on two consecutive visits.

The fox is lazy: travel distances must strictly decrease. The distance from the origin to the first treat is greater than the distance from the first to the second treat, and so on.

What is the maximum number of treats the fox can collect?

The first line contains N (1 ≤ N ≤ 2000). Each of the next N lines has Xi and Yi (−10 000 ≤ Xi, Yi ≤ 10 000), the coordinates of the ith neighbor.

Print one integer, the maximum number of treats.