# Gopher II

Time Limit: 2000MS

Memory Limit: 65536K

## Description

The gopher family, having averted the canine threat, must face a new predator. The are n gophers and m gopher holes, each at distinct (x, y) coordinates. A hawk arrives and if a gopher does not reach a hole in s seconds it is vulnerable to being eaten. A hole can save at most one gopher. All the gophers run at the same velocity v. The gopher family needs an escape strategy that minimizes the number of vulnerable gophers.

## Input

The input contains several cases. The first line of each case contains four positive integers less than 100: n, m, s, and v. The next n lines give the coordinates of the gophers; the following m lines give the coordinates of the gopher holes. All distances are in metres; all times are in seconds; all velocities are in metres per second.

## Output

Output consists of a single line for each case, giving the number of vulnerable gophers.

## Sample Input

2 2 5 10
1.0 1.0
2.0 2.0
100.0 100.0
20.0 20.0

## Sample Output

1


## Source

Waterloo local 2001.01.27