| A top-secret algorithmic research facility has decided to up its security by | |
| hiring guards to keep watch over the premises. After all, they don't want | |
| anyone sneaking in and learning the answers to questions such as "does P = | |
| NP?" and "what are the solutions to the 2016 Facebook Hacker Cup problems?". | |
| When viewed from above, the facility can be modeled as a grid **G** with 2 | |
| rows and **N** columns. The **j**th cell in the **i**th row is either empty | |
| (represented by **Gi,j** = ".") or occupied by a building (**Gi,j** = "X"), | |
| and the grid includes at least one empty cell. | |
| Guards may be potentially stationed in any of the empty cells. A guard can see | |
| not only their own cell, but also all contiguous empty cells in each of the 4 | |
| compass directions (up, down, left, and right) until the edge of the grid or a | |
| building. For example, in the grid below, the guard ("G") can see every cell | |
| marked with an asterisk ("*"): | |
| .*.X.X.. | |
| *G*****X | |
| What is the minimum number of guards required such that every empty cell in | |
| the grid can be seen by at least one of them? | |
| ### Input | |
| Input begins with an integer **T**, the number of facilities that need | |
| guarding. For each facility, there is first a line containing the integer | |
| **N**. The next line contains the grid cells **G1,1** to **G1,N** in order. | |
| The third line contains the grid cells **G2,1** to **G2,N** in order. | |
| ### Output | |
| For the **i**th facility, print a line containing "Case #**i**: " followed by | |
| the number of guards required to guard the facility. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 200 | |
| 1 ≤ **N** ≤ 1,000 | |
| ### Explanation of Sample | |
| In the first case, one solution is to place three guards as follows: | |
| .G.X.XG. | |
| ....G..X | |