### Problem Statement

A medieval city consists of square blocks, each of equal size, situated on a grid. The blocks form a connected figure with no holes. An example of such a city is shown in the picture below.

The red line shows the boundary of the city. Each block has a danger value that is assigned as follows. Blocks that have the city boundary as a side are called 0-dangerous. Blocks that are adjacent to 0-dangerous blocks and have not yet been assigned a danger value are called 1-dangerous. Two blocks are considered adjacent if they share a side. Blocks that are adjacent to 1-dangerous blocks and have not yet been assigned a danger value are called 2-dangerous blocks, and so on. In the picture above, all 0-dangerous and 1-dangerous blocks are colored dark gray.

We can represent a city as a string of letters 'R', 'L', 'U', 'D' (right, left, up, down) describing a walk along its boundary in the clockwise or counter-clockwise direction. Each letter represents the length of a single block's side. Multiple consecutive equal letters can be written using a simple compression method. An integer K that immediately follows a letter means that the letter is repeated K times. For example, the city in the picture above can be described by the string "LUUR7D4RDLDDDL7UURU2UU". Obviously there can be multiple strings that describe the same city.

You are given a String[] boundary and an int dangerBound. Concatenate all the elements of boundary to get the string description of a city. Return the number of i-dangerous blocks in the city where i <= dangerBound.

### Definition

 Class: MedievalCity Method: getDangerousBlocks Parameters: String[], int Returns: int Method signature: int getDangerousBlocks(String[] boundary, int dangerBound) (be sure your method is public)

### Constraints

-boundary will contain between 1 and 50 elements, inclusive.
-Each element of boundary will contain between 1 and 50 characters, inclusive.
-Each element of boundary will contain only the letters 'R', 'L', 'U', 'D', and digits ('0'-'9').
-Each sequences of digits in the concatenation of all the elements of boundary will be an integer without leading zeroes between 1 and 50, inclusive.
-boundary will describe a correct closed boundary that does not touch or intersect itself.
-dangerBound will be between 0 and 10, inclusive.

### Examples

0)

 `{"LURD"}` `0`
`Returns: 1`
 This city contains only a single square block.
1)

 `{"LUUR7D4RDLDDDL7UURU2UU"}` `1`
`Returns: 44`
 The example from the problem statement.
2)

 `{"L50U50R50D50"}` `10`
`Returns: 1716`
3)

 `{"L50U50U50U50U50R50D50D50D50D50"}` `7`
`Returns: 3744`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7506

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10743&pm=7506

Mike Mirzayanov

#### Testers:

PabloGilberto , brett1479 , vorthys , Olexiy

Graph Theory