hackercupai/hackercup huggingface dataset:
There has been a war between the digits in the kingdom of numbers and it is
King Infinity's job to restore balance. In search of peace he came up with a
new number system which only allows those numbers to exist in which:

1\. None of the consecutive digits are at war against each other.

2\. No two digits that have only one digit in between them are at war.

For example, if 4 is at war with 5, then 45, 405, and 574 are all forbidden.

A digit can be at war with itself. You are given a 10 x 10 binary matrix **M**
(0 index based), where **M**[i][j] denotes whether there is a war between
digit i and digit j. If **M**[i][j] = 1 then they are at war and **M**[i][j] =
0 means they are not. **M**[i][j] will always be equal to **M**[j][i].

Your task is to find the count of positive numbers that can exist in this
number system with number of digits ≤ **K**. No number in the number system
can have leading zeroes.

## Limits

1 ≤ **K** ≤ 1018

## Input

Input consists of **T** test cases, with **T** ≤ 25. Each test case begins
with the value of **K** followed by a 10x10 binary matrix.

## Output

For every test case output the result modulo 109 +7