### Problem Statement

We have a book with N pages, numbered 1 to N. How many times does each digit occur in the page numbers?

You are given an int N. Return a int[] with 10 elements, where for all i between 0 and 9, inclusive, the element i will be the number of times digit i occurs when we write down all the numbers between 1 and N, inclusive.

### Definition

 Class: PageNumbers Method: getCounts Parameters: int Returns: int[] Method signature: int[] getCounts(int N) (be sure your method is public)

### Notes

-You may assume that for any valid input each of the output values fits into an int.

### Constraints

-N will be between 1 and 1,000,000,000, inclusive.

### Examples

0)

 `7`
`Returns: {0, 1, 1, 1, 1, 1, 1, 1, 0, 0 }`
 The page numbers in this case are simply 1, 2, 3, 4, 5, 6, and 7.
1)

 `11`
`Returns: {1, 4, 1, 1, 1, 1, 1, 1, 1, 1 }`
 In comparison to the previous case, we added the pages 8, 9, 10, and 11. Now we have each digit exactly once, except for the digit 1 that occurs four times: once in 1 and 10, and twice in 11.
2)

 `19`
`Returns: {1, 12, 2, 2, 2, 2, 2, 2, 2, 2 }`
 Digits 2 to 9 now occur twice each, and we have plenty of occurrences of the digit 1.
3)

 `999`
`Returns: {189, 300, 300, 300, 300, 300, 300, 300, 300, 300 }`
 Due to symmetry, each of the digits 1 to 9 occurs equally many times in the sequence 1,2,...,999.
4)

 `543212345`
```Returns:
{429904664, 541008121, 540917467, 540117067, 533117017, 473117011, 429904664, 429904664, 429904664, 429904664 }```
 Watch out for the time limit.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10329

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13757&pm=10329

misof

#### Testers:

PabloGilberto , marian , ivan_metelsky

#### Problem categories:

Brute Force, Recursion, Simple Math, Simple Search, Iteration