Strategic Bombing

The enemy relies heavily on transporting supplies and personnel between two specific points, A and B. Points A and B, along with other points C, D, E, and so on, are linked by a network of roads. Your mission, should you choose to accept it, is to identify every road that could be bombed to cut off all traffic between A and B.

Input

Each point is identified by a single uppercase letter, so there are at most 26 points. Each line of input names a pair of points joined by a road, written as the two letters with no separator. The end of the input is marked by a line containing **.

All roads are two-way, so road AC is the same as road CA. There is at most one road between any pair of points.

Output

Print every road whose removal would halt all traffic between A and B, that is, every road that lies on all routes from A to B. Print these roads in the same order they appear in the input, one per line, using the same two letters in the same order the input gave them.

After the list, print a line There are n disconnecting roads., where $n$ is the number of such roads. If there is no such road, print There are 0 disconnecting roads.