On the plane are given \( k+n\) distinct lines , where \( k>1\) is integer and \( n\) is integer as well.Any three of these lines do not pass through the same point . Among these lines exactly \( k\) are parallel and all the other \(n\) lines intersect each other. All \( k+n\) lines define on the plane a partition of triangular , polygonic or not bounded regions. Two regions are called different, if they don't have common points or if they have common points only on their boundary. A region is called ''good'' if it is contained in a zone between two parallel lines .
If in a such given configuration the minimum number of ''good'' regions is \( 176\) and the maximum number of these regions is \( 221\), find \(k+n\).This problem is part of this set.