Task:

You are given two strings S₁ and S₂ that can contain any ASCII symbols, except for the line feed character.

Normalize the strings: delete all symbols that are not latin letters, digits or a whitespace character, and decapitalize every letter (make it lowercase). You should then delete all words which length is less or equal to 3 and all extra whitespace characters (so that there's no more than one whitespace character between two words).

For the resulting strings count the following value: c / (|S₁| + |S₂| - c), where c is the number of matching symbols between the strings S₁ and S₂ and |S_n| is the length of the n-th string.

Input:

Two strings S₁ and S₂  separated with a line feed character.

Output:

The calculated value with at least 10^-6 accuracy.

Example: