Farmer John's cows enjoy reading books, and FJ has discovered that his cows produce more milk when they read books of a somewhat intellectual nature. He decides to update the barn library to replace all of the cheap romance novels with textbooks on algorithms and mathematics. Unfortunately, a shipment of these new books has fallen in the mud and their ISBN numbers are now hard to read.
An ISBN (International Standard Book Number) is a ten digit code that uniquely identifies a book. The first nine digits represent the book and the last digit is used to make sure the ISBN is correct. To verify that an ISBN number is correct, you calculate a sum that is 10 times the first digit plus 9 times the second digit plus 8 times the third digit ... all the way until you add 1 times the last digit. If the final number leaves no remainder when divided by 11, the code is a valid ISBN.
For example 0201103311 is a valid ISBN, since
10*0 + 9*2 + 8*0 + 7*1 + 6*1 + 5*0 + 4*3 + 3*3 + 2*1 + 1*1 = 55.
Each of the first nine digits can take a value between 0 and 9. Sometimes it is necessary to make the last digit equal to ten; this is done by writing the last digit as X. For example, 156881111X is a valid ISBN number.
Your task is to fill in the missing digit from a given ISBN number where the missing digit is represented as '?'.
- Line 1: A single line with a ten digit ISBN number that contains '?' in a single position
- Line 1: The missing digit (0..9 or X). Output -1 if there is no acceptable digit for the position marked '?' that gives a valid ISBN.