Triangle $$ABC$$ is isosceles with $$AC = BC$$ and $$\angle ACB = 106^\circ.$$ Point $$M$$ is in the interior of the triangle so that $$\angle MAC = 7^\circ$$ and $$\angle MCA = 23^\circ.$$ Find the number of degrees in $$\angle CMB.$$

(第二十一届AIME1 2003 第10题)