A robot is standing on the bottom left vertex $(0,0)$ of a $5 \times 5$ grid and wants to go to $(5,5)$, only moving to the right $(a,b) \mapsto (a+1,b)$ or upward $(a,b) \mapsto (a,b+1)$. However, this robot is not programmed perfectly and sometimes takes the upper-left diagonal path $(a,b) \mapsto (a-1,b+1)$. As the grid is surrounded by walls, the robot cannot go outside the region $0 \leq a,b \leq 5$. Supposing that the robot takes the diagonal path exactly once, compute the number of different routes the robot can take.

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