Edward starts at his house located at \((0,0)\) and needs to reach the point \((6,4)\), which is the coordinate for his school. However, there is a park shaped as a square with coordinates \((2,1), (2,3), (4,1), (4,3)\). Edward cannot walk inside the park, but there is a road along the perimeter of the square. Determine how many different shortest routes exist from Edward's house to his school.

Let's think step by step and output the final answer within \boxed{}.
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