[Solution] Rubik’s Cube Coloring (easy version) solution codeforces

Rubik’s Cube Coloring (easy version) solution codeforces


It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.

Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?

Rubik’s Cube Coloring (easy version) solution codeforces

You have a perfect binary tree of 2π‘˜βˆ’12kβˆ’1 nodesΒ β€” a binary tree where all vertices 𝑖i from 11 to 2π‘˜βˆ’1βˆ’12kβˆ’1βˆ’1 have exactly two children: vertices 2𝑖2i and 2𝑖+12i+1. Vertices from 2π‘˜βˆ’12kβˆ’1 to 2π‘˜βˆ’12kβˆ’1 don’t have any children. You want to color its vertices with the 66 Rubik’s cube colors (White, Green, Red, Blue, Orange and Yellow).

Let’s call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik’s cube.

Rubik's Cube Coloring (easy version) solution codeforces

A picture of Rubik’s cube and its 2D map.

More formally:

  • a white node can not be neighboring with white and yellow nodes;
  • a yellow node can not be neighboring with white and yellow nodes;
  • a green node can not be neighboring with green and blue nodes;
  • a blue node can not be neighboring with green and blue nodes;
  • a red node can not be neighboring with red and orange nodes;
  • an orange node can not be neighboring with red and orange nodes;

You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.

The answer may be too large, so output the answer modulo 109+7109+7.

Rubik’s Cube Coloring (easy version) solution codeforces

Input

The first and only line contains the integers π‘˜k (1β‰€π‘˜β‰€601≀k≀60)Β β€” the number of levels in the perfect binary tree you need to color.

Rubik’s Cube Coloring (easy version) solution codeforces

Output

Print one integerΒ β€” the number of the different colorings modulo 109+7109+7.

Examples
input

Copy
3
output

Copy
24576

Rubik’s Cube Coloring (easy version) solution codeforces

input

Copy
14

Rubik’s Cube Coloring (easy version) solution codeforces

output

Copy
934234

Rubik’s Cube Coloring (easy version) solution codeforces

Note

In the picture below, you can see one of the correct colorings of the first example.



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