### Problem Statement

You have a machine that cuts glass panes using a robotic arm with a diamond point at the end.

The input to the machine is a rectangular piece of glass with width W and height H. The machine has a coordinate system with point (0,0) in one corner of the glass pane and (W,H) in the opposite corner. In the beginning, the diamond point is positioned at (startx,starty). Then the machine executes a given program.

The program is given as a String[] program. Concatenate the elements of program to get one long string that describes the program. Each character in the program describes one movement of the diamond point: 'L' decreases its x-coordinate, 'R' increases its x-coordinate, 'U' decreases its y-coordinate and 'D' increases its y-coordinate by 1. During all movements, the diamond point cuts the glass.

Once the cutting is over, the glass may fall apart into multiple pieces. Compute and return their count.

### Definition

 Class: CuttingGlass Method: pieces Parameters: int, int, int, int, String[] Returns: int Method signature: int pieces(int W, int H, int startx, int starty, String[] program) (be sure your method is public)

### Constraints

-W will be between 1 and 1000, inclusive.
-H will be between 1 and 1000, inclusive.
-startx will be between 0 and W, inclusive.
-starty will be between 0 and H, inclusive.
-program will contain between 1 and 50 elements, inclusive.
-Each element of program will contain between 1 and 50 characters, inclusive.
-Each character in each element of program will be one of 'L', 'R', 'U', and 'D'.
-The program will be such that the diamond point never leaves the glass pane, but it may touch the boundary and even cut along the boundary.

### Examples

0)

 `100` `100` `50` `50` `{"ULDR"}`
`Returns: 2`
 This program cuts out a small square piece from a large plate.
1)

 `10` `10` `3` `4` `{"UDUDUDUDUDU"}`
`Returns: 1`
 After this program is executed, there will be a short cut on the glass pane, but it will still be in one piece.
2)

 `3` `3` `0` `0` `{"RDDDUUU","RDDDUUU","R","DLLLRRR","DLLL"}`
`Returns: 9`
 This program cuts a 3x3 glass pane into nine separate 1x1 squares.
3)

 `5` `3` `5` `3` `{"LULLULLU"}`
`Returns: 2`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10929

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14278&pm=10929

misof

#### Testers:

PabloGilberto , ivan_metelsky , zhuzeyuan

#### Problem categories:

Geometry, Graph Theory, Simulation