Sunday, July 31, 2016

TCS Code Vita Season-5 Round-1 set-2 Program-8

3D Maze problem

Suppose, an ant is trapped in a maze, with only one way in and one way out.

The maze is a cubic-lattice like structure of dimension NxNxN (Length=Breadth=Height=N). The way in is the left-bottom most point, and the way out is the right top-most point (along the principal diagonal). The below picture shows the maze for N=2. 



        
Figure 1. 
Assuming the ant only moves right, forward or upwards along the grids of the maze, calculate the total number of ways in which the ant can escape. Mathematically right, forward and upwards are defined at positive changes in co-ordinates on x, y and z axes respectively. 

Example:
For, N=1, the grid structure and solution is shown below: 




        
Figure 2. 


Thus, for N=1, we have a net of 6 ways. 


Input Format:

Single integer N 
Output Format:

Output also consists of a single number corresponding to the number of ways the ant can escape the maze.
Constraints:
  • 0<N<=8

Example
Example Number
Sample Input
Sample Output
1
1

6
2
2

90













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