Again A + B

Consider a set of strings made up exclusively of lowercase Latin letters and decimal digits. We define two such strings as similar if:

1. They are of the same length;

2. Characters at corresponding positions in these strings are either both letters or both digits.

For all strings similar to a given one, we define an addition operation. By arranging all similar strings in reverse lexicographical order, each string can be assigned an ordinal number starting from zero. Let N(A) represent the ordinal number of string A, and N(B) represent the ordinal number of string B. The sum of strings A and B is defined as the string whose ordinal number in this sequence is (N(A) + N(B)) mod M, where M is the total number of strings similar to the ones being added.

Input

The first line contains string A, and the second line contains string B.

Each string has a length of at least 1 and no more than 300,000. The input guarantees that the strings meet the similarity condition described above.

Output

Output a single line containing the result of adding the given strings.

Examples