Convex quadrilateral $ABCD$ satisfies $\angle{CAB} = \angle{ADB} = 30^{\circ}, \angle{ABD} = 77^{\circ}, BC = CD$ and $\angle{BCD} =n^{\circ}$ for some positive integer $n$. Compute $n$.

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