Table of Contents

## Rubik’s Cube Coloring (hard version) solution codeforces

It is the hard version of the problem. The difference is that in this version, there are 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?

**You have a perfect binary tree of 2πβ12kβ1 nodesΒ β a binary tree where all vertices πi from 11 to 2πβ1β12kβ1β1 have exactly two children: vertices 2π2i and 2π+12i+1. Vertices from 2πβ12kβ1 to 2πβ12kβ1 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;

However, there are πn special nodes in the tree, colors of which are already chosen.

**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 (hard version) solution codeforces

The first line contains the integers πk (1β€πβ€601β€kβ€60)Β β the number of levels in the perfect binary tree you need to color.

The second line contains the integer πn (1β€πβ€min(2πβ1,2000)1β€nβ€min(2kβ1,2000))Β β the number of nodes, colors of which are already chosen.

The next πn lines contains integer π£v (1β€π£β€2πβ11β€vβ€2kβ1) and string π sΒ β the index of the node and the color of the node (π s is one of the white, yellow, green, blue, red and orange).

It is guaranteed that each node π£v appears in the input at most once.

### Rubik’s Cube Coloring (hard version) solution codeforces

Output

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

### Rubik’s Cube Coloring (hard version) solution codeforces

Examples

3 2 5 orange 2 white

1024

### Rubik’s Cube Coloring (hard version) solution codeforces

input

2 2 1 white 2 white

0

### Rubik’s Cube Coloring (hard version) solution codeforces

input

10 3 1 blue 4 red 5 orange

328925088

### Rubik’s Cube Coloring (hard version) solution codeforces

Note

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