A valid move in the puzzle is moving one disk from the top of one (source) peg to the top of the other (destination) peg, with a constraint that a disk can be placed only onto an empty destination peg or onto a disk of a larger diameter. We denote a move with two capital letters - the first letter denotes the source disk, and the second letter denotes the destination disk. For example, AB is a move from disk A
The puzzle is considered solved when all the disks are stacked onto either peg B
All six potential moves in the game (AB, AC, BA, BC, CA, and CB) are arranged into a list. The order of moves in this list defines our strategy. We always make the first valid move from this list with an additional constraint that we never move the same disk twice in a row.
It can be proven that this algorithm always solves the puzzle. Your problem is to find the number of moves it takes for this algorithm to solve the puzzle using a given strategy.
The input file contains two lines. The first line consists of a single integer number n
Write to the output file the number of moves it takes to solve the puzzle. This number will not exceed 1018
Input
n
30)
Output
Sample Input
3
AB BC CA BA CB AC
2
AB BA CA BC CB AC
Sample Output
7
5