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 2k−12k−1 nodes — a binary tree where all vertices ii from 11 to 2k−1−12k−1−1 have exactly two children: vertices 2i2i and 2i+12i+1. Vertices from 2k−12k−1 to 2k−12k−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.

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

• 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;
• Rubik’s Cube Coloring (easy version) solution codeforces

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.