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Let's define the distance between two strings of equal length, S_A and S_B, as d(S_A, S_B). This distance is calculated by summing, for each position i (where 1 ≤ i ≤ |S_A|), the shortest distance between the characters S_A(i) and S_B(i) in a cyclically closed Latin alphabet. In this alphabet, the sequence wraps around, so after "a" comes "b", ..., and after "z" comes "a". For example, d(aba, aca) = 1, and d(aba, zbz) = 2.
A cyclic shift of a string S is a transformation (denoted as S → k) that rearranges the string into S_kS_{k+1}S_{k+2}...S_{|S|}S_1S_2...S_{k-1} for some k, where |S| is the length of S.
The degree of cyclic distance between strings S_A and S_B (where |S_A| = |S_B|) is defined as the sum:
Your task is to calculate the degree of cyclic distance for the given strings S_A and S_B.
Input
The first and second lines each contain a string of equal length, not exceeding 100000 characters. The strings consist solely of lowercase Latin letters.
Output
Output the result of the calculation.