Baltic Olympiad in Informatics: 2013 Day 1, Problem 2

A string is a palindrome if it remains the same when it is read backwards. A number is palindrome-free if it does not contain a palindrome with a length greater than ~1~ as a substring. For example, the number ~16\,276~ is palindrome-free whereas the number ~17\,276~ is not because it contains the palindrome ~727~.

Your task is to calculate the total number of palindrome-free numbers in a given range.

Input

The input contains two integers, ~a~ and ~b~.

Output

The output should contain one integer: the total number of palindrome-free numbers in the range ~a, \dots, b~ (including ~a~ and ~b~).

Constraints

~0 \le a \le b \le 10^{18}~

In test cases worth ~25~ points: ~b-a \le 100\,000~.

Sample Input 1

123 321

Sample Output 1

153

Sample Input 2

123456789 987654321

Sample Output 2

167386971