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)