Minimum cost to make two words equal

We are given two words $s$ and $t$ made up of only lowercase letters, and we must make them equal. We can only perform two kind of operations, as many times as needed: Remove a letter, with cost 3, and duplicate a letter, with cost 2. What is the minimum possible cost?

For example, for $s=$ “aaba” and $t=$ “abb” the minimum cost is 7, which corresponds to duplicating the ‘b’ and removing the last ‘a’ of $s$, and duplicating the ‘a’ of $t$.

Input

Input consists of several cases with $s$ and $t$, both with between 1 and 1000 letters.

Output

For every case, print the minimum cost to make the two words equal.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T10:23:18.416Z

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