Consider the set of strings consisting only of decimal digits or Latin alphabet letters of both cases. Two strings are considered similar if they have the same length and, additionally, at the same positions have symbols of the same category, with the categories being – digits, lowercase Latin letters, and uppercase Latin letters.
For each set consisting of similar strings, the subtraction operation is defined. We order all strings similar to the given one in lexicographic order and then number them starting from zero. The result of subtracting string from string is defined as a string that satisfies:
where is the total number of similar strings, and , , and are the numbers of strings , , and , respectively, as ordered above. The \mod operation is understood in the usual mathematical sense – it is the smallest non-negative number such that the result equals (N(A) - N(B)) modulo .
The first line of the input contains string , and the second line contains string . It is guaranteed that and are similar and their lengths are at least and no more than .
Output a single line – the answer to the problem ().
Example 1