Minimum Operations for Lexicographical Superiority

Devu has two strings: \(s\) and \(t\). His goal is to make \(s\) lexicographically greater than \(t\) by performing a minimal operation. In one operation, he can choose an index \(i\) (0-indexed) where \(s[i] \le t[i]\) and replace \(s[i]\) with the smallest character that is strictly greater than \(t[i]\) (i.e. replace \(s[i]\) with \(\text{chr}(\text{ord}(t[i])+1)\)).

If \(s\) is already lexicographically greater than \(t\), no operations are needed. Your task is to determine the minimum number of operations required to achieve this goal.

Note: The two strings are assumed to be of the same length.

Example:
For \(s = \texttt{abc}\) and \(t = \texttt{bcd}\), replacing \(s[0]\) (because \(\texttt{'a'} \le \texttt{'b'}\)) with \(\texttt{'c'}\) makes \(s\) become \(\texttt{cbc}\) which is lexicographically greater than \(\texttt{bcd}\). Hence, the answer is 1.

inputFormat

The input consists of two lines:

1. The first line contains the string \(s\).
2. The second line contains the string \(t\).

Both strings are guaranteed to be of the same length and contain only lowercase English letters.

outputFormat

Output a single integer denoting the minimum number of operations required so that the string \(s\) becomes lexicographically greater than \(t\). The result should be printed to stdout.

abc
bcd

1