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

