Distinct points \(A\) and \(B\) are on a semicircle with diameter \(MN\) and center \(C\). The point \(P\) is on \(CN\) and \(\angle CAP = \angle CBP = 10^{\circ}\). If \(\stackrel{\frown}{MA} = 40^{\circ}\), then \(\stackrel{\frown}{BN}\) equals how many degrees? Please provide your answer as an integer representing the number of degrees.

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