| 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 | |