New Hanoi Tower

The rules of the new Hanoi tower game are as follows.

• There are three rods: rod A, rod B, and rod C.
• When the game starts, each rod holds zero or more disks.
• All disks have the same size, and each disk is of type A, B, or C. A disk of type A is called disk A, and the other two types are named the same way.
• One move takes the topmost disk of one rod and places it on top of another rod.
• The goal is to leave only disk A on rod A, only disk B on rod B, and only disk C on rod C.

Given the starting contents of the three rods, write a program that finds the minimum number of moves needed to reach the goal.

The first line contains the number of disks on rod A and the contents of rod A. The second line contains the number of disks on rod B and the contents of rod B. The third line contains the number of disks on rod C and the contents of rod C.

The contents of a rod are written from the bottom disk upward as a string made only of the characters A, B, and C. A rod with no disks is given as the number 0 with no string after it. The total number of disks on the three rods is at least 1 and at most 10.

Print the minimum number of moves needed to reach the goal on one line.

A state where rod A holds one disk B, rod B holds one disk C, and rod C holds one disk A takes five moves.

• Move disk A to rod A
• Move disk C to rod C
• Move disk A to rod C
• Move disk B to rod B
• Move disk A to rod A

A state where rod A holds disk C, disk B, and disk A from the bottom up while the other two rods are empty also takes five moves.

• Move disk A to rod C
• Move disk B to rod B
• Move disk A to rod B
• Move disk C to rod C
• Move disk A to rod A