JOIN

 Problem Statement

Problem Statement for TBlocks

### Problem Statement

Fox Ciel has an unlimited supply of T-shaped tetrominoes. We will call them T-blocks. One T-block is shown in the picture below. The green cell is called the center of the T-block.

Ciel also has a rectangular board divided into square cells. The cells of the board have the same size as the cells of her T-blocks. Each cell is marked 'o', '*', or '-'. Ciel wants to place some T-blocks onto this board in a way that satisfies the following conditions:

• Each T-block covers precisely 4 cells of the board. (Thus, each T-block must be placed completely inside the board.)
• No two T-blocks overlap. (They are allowed to touch each other.)
• The center of a T-block can only be placed on cells marked 'o' and '*'.
• Each 'o' cell has to contain the center of some T-block.

You are given a String[] board that represents Ciel's board using the characters specified above. Return the number of valid ways in which T-blocks can be placed onto this board, modulo 1,000,000,007.

### Definition

 Class: TBlocks Method: count Parameters: String[] Returns: int Method signature: int count(String[] board) (be sure your method is public)

### Constraints

-board will contain between 1 and 50 elements, inclusive.
-Each element of board will contain between 1 and 50 characters, inclusive.
-Each element of board will contain the same number of characters.
-Each character of each element of board will be 'o', '*' or '-'.
-board will contain between 0 and 500 'o's, inclusive.
-board will contain between 0 and 12 '*'s, inclusive.

### Examples

0)

 ```{"---" ,"-o-" ,"---"}```
`Returns: 4`
 We have to place exactly one T-block. Its center has to be on the middle cell. There are 4 ways to do this:
1)

 `{"o"}`
`Returns: 0`
 There isn't enough space to place a T-block here.
2)

 ```{"**-" ,"-**"}```
`Returns: 3`
 Some '*' cells may remain empty. They may also contain T-block cells other than the center.
3)

 ```{"----" ,"-o*-" ,"--*-" ,"----"}```
`Returns: 7`
4)

 ```{"--" ,"--" ,"--"}```
`Returns: 1`
5)

 ```{"-----o------o-----o---o------o-----o--------------" ,"-o--------o---o-----------o----o-----o--o---o-o--o" ,"----o-o-o--o-------*-o---o--o---o--o---o--o-------" ,"-o-----------o-oo-------------o------o---------o--" ,"---o-o-o--o-------o-o--o--o------oo-----o---*--o--" ,"--o---------o-o-------------o--o-----o---o-------o" ,"o---o---oo---------o--o--o-------------o---*------" ,"--o---o------o---o---------*-o--o-o------o---o-oo-" ,"------o---o----o-----o--o------------o------------" ,"-o-o----o---o-----o-------o---oo---o----o--o--o---" ,"------o-------o-o----o--o---o----o---o----------o-" ,"----o----oo--------o-o----o---o----o---o----o--o--" ,"--o-----------o-----------o-----o---------o------o" ,"o-----o-----o----o-----o----o----o---o------o-o---" ,"---o-----o-----o----o----o----o--------o--------o-" ,"-o----o------o----o-----o---o---o---o----o-----o--" ,"--------o--o----o----o-------o--------o-----o----o" ,"----o-----o---o---oo---o-o-----o--o------o----o---" ,"-o----o-o----o--o----o-----o--------o--o---o--o-o-" ,"---o------------o--o--------------o---------------" ,"-----o-o--o---o--------o--*--o--o----o---o-o---o--" ,"-o-------o-------o---o--o----------o---o----o-----" ,"----o-o-----o--o---o-------o--o------o----o-----o-" ,"-o--------o---------o--o-o------o--o-----*----o---" ,"-----o-o-----o--o-o---------o------o---o----------" ,"-o-o-----o-o-------o--o--o----o------o--o---o--o-o" ,"------o--------o-o-----o----o---o-*---------------" ,"-o--o-----o---------o-----------------o---*o----o-" ,"----o---o---o-o---o-----o--o---oo--o----o----o----" ,"------*----o---------o-------o--------o----------o" ,"o--*-----o-----o---o---o---o--o--o--o----o--o-oo--" ,"--o----o---o-----o-------o-------------o-o--------" ,"----o----o---o-o-----o----o-----o-o--o-------o--o-" ,"------o---o-------------o---o-o---------o--o------" ,"-o--o-------o-o--o-o--o---------o--o-o-----o--o---" ,"------o-o--------o-------o---o---------o--------o-" ,"--o----------o-o-----o-----o------o-o-----o--o----" ,"---------o-o------o----o------o---------o--o-----o" ,"o--o-o----------o---o----o---o--o--o--o-------o---" ,"-------o---oo-o-------o----o---o--o-----o-o-----o-" ,"-o--o---o-------o--o----o----o------oo-------o----" ,"-----o----o----------*-----o-----o------o-o-------" ,"o-o----o----o---o--o---o-----o-o------o-----o-o-o-" ,"----o----o----o-------o---o-------o-o----o--o-----" ,"-o----o----o------o-----------o--------o------o--o" ,"-----o--o---o--o----o----oo-o---o-----o----o------" ,"o--o------o-------o----o----------*--------o----o-" ,"-------o-o---o-------o-------o--o---o----o----o---" ,"-o--oo----------oo-o----o--o-----------o----o----o" ,"--------o--o--o-------o-------o---o--o---o-----o--"}```
`Returns: 481632789`

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This problem was used for:
2013 TCO Algorithm Championship Round - Division I, Level Three