### Problem Statement

There are some rectangles on a plane, with sides parallel to the axes. They may intersect and overlap. You are to place a rectangle q on this plane (its sides must also be parallel to axes) and want to cover the maximum possible number of rectangles.

You are given a String[] rectangles, each element of which is formatted as "X1 Y1 X2 Y2", where X1 and Y1 are the coordinates of the lower left corner of a rectangle, and X2 and Y2 are the coordinates of the upper right corner. You are given the lengths of the sides of q - qa and qb. You are to return the maximum number of rectangles that can be covered by q. A rectangle is covered by q if it lies fully inside q (for example, "1 1 2 2" is covered by "-1 1 2 100").

### Definition

 Class: OneMoreRectangle Method: maxCover Parameters: String[], int, int Returns: int Method signature: int maxCover(String[] rectangles, int qa, int qb) (be sure your method is public)

### Notes

-The rectangle you place may be oriented in either of the two possible ways.

### Constraints

-rectangles will contain between 0 and 50 elements, inclusive.
-Each element of rectangles will be formatted as "X1 Y1 X2 Y2".
-X1, Y1, X2, and Y2 will each be an integer between -1000000000 and 1000000000, inclusive, with no extra leading zeros.
-X2 will be greater than X1, and Y2 will be greater than Y1.
-qa and qb will be between 1 and 1000000000 inclusive.

### Examples

0)

 `{"1 1 2 2","2 2 3 3","3 3 4 4"}` `2` `2`
`Returns: 2`
 q is 2x2, so it may cover the first and second rectangles, or the second and third ones - answer is 2.
1)

 `{"1 1 5 5","1 1 4 2","1 1 2 4", "2 3 5 5"}` `3` `3`
`Returns: 2`
 q may cover "1 1 4 2" and "1 1 2 4".
2)

 `{"1 1 4 2","1 2 2 5","4 1 5 4","2 4 5 5"}` `3` `3`
`Returns: 1`
3)

 `{"1 1 4 2","1 2 2 5","4 1 5 4","2 4 5 5"}` `4` `4`
`Returns: 4`
4)

 ```{"1 4 6573 345","23 4366 23545 366783","54 7895 2565 23567","3456 345 475457 45767654", "-234 -654885 0 0","-32654 -43256 -34 -5463","-10000 -10000 10000 10000"}``` `100000` `100000`
`Returns: 4`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4590

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=7226&pm=4590

Vedensky

#### Testers:

PabloGilberto , lbackstrom , brett1479

Brute Force