IMAS 2022–2023 Junior Division — First Round Question 20

Let $P$ be the point in the interior of triangle $ABC$ such that $\angle BAP=13^\circ$, $\angle CAP=31^\circ$, $\angle ACP=44^\circ$ and $AP=BC$, as shown in the diagram below. What is the measure, in degrees, of $\angle BCP$?