Given an axis-aligned rectangle with vertices at and and closed disks of radius 100, determine if there exists a path starting at and ending at where and where the path does not visit a point strictly outside the given rectangle or touching any of the disks.

In the event no such path exists, compute the minimum number of disks to remove such that a path can be constructed without exiting the rectangle or touching the remaining disks.

#### Constraints

#### Input Specification

The first line will contain three space-separated integers, , , and .

Each of the next lines contains a pair of integers and , indicating a center of one of the disks.

#### Output Specification

Print, on a single line, the minimum number of disks to remove such that there exists a path connecting the left side of the rectangle to the right side of the rectangle that does not exit the rectangle or touch any of the disks.

#### Sample Input

```
130 340 5
10 50
130 130
70 170
0 180
60 260
```

#### Sample Output

`1`

## Comments