Game: Pattern

Solve the following Pattern puzzle. You are given a 2D ASCII board representation. 

Legend:
-"+" for vertices
-"-" for horizontal edges
-"|" for vertical edges
-Spaces for empty cells
-Digits on top and left sides of the grid (called "clues") indicating how many cells in that row or column should form a connected pattern. 



Rules:
Patterns are formed by placing "##" into cells that should be filled and ".." into cells that should stay empty. For example when there are two clues of "3" in a row, it means that there should be two separate groups of three connected ## cells in that row. 
Only place ## and .. in empty cells (spaces). Do not modify or move any of the existing +, -, |, or numbers. Each row and column must contain exactly the number of connected ## groups as indicated by the clues. The pattern must be continuous (all ## cells must be connected horizontally or vertically).

Think step by step then output only the solved board in json format as shown below.

Output Format:

Return your final answer exactly like this:

```json
{"response": "{final board state}"}
```

Example Puzzle:

Input:

       2  1  4  2  4 
     +--+--+--+--+--+
    3|  |  |  |  |  |
     +--+--+--+--+--+
    3|  |  |  |  |  |
     +--+--+--+--+--+
  1 1|  |  |  |  |  |
     +--+--+--+--+--+
1 1 1|  |  |  |  |  |
     +--+--+--+--+--+
    2|  |  |  |  |  |
     +--+--+--+--+--+

Solution:

```json
{"response": "
       2  1  4  2  4 
     +--+--+--+--+--+
    3|..|..|##|##|##|
     +--+--+--+--+--+
    3|..|..|##|##|##|
     +--+--+--+--+--+
  1 1|..|..|##|..|##|
     +--+--+--+--+--+
1 1 1|##|..|##|..|##|
     +--+--+--+--+--+
    2|##|##|..|..|..|
     +--+--+--+--+--+
"}```

Now solve this puzzle: