The one of the edition distance (II)

At this stage, you surely already know that some problems are so classic
that blah, blah, blah. Nothing new with this problem. Now, we ask you to
compute the minimum cost to insert letters into or to modify letters
from two words w₁ and w₂ to make them identical. Both words are made up
of only letters chosen among the n smallest lowercase letters (for
instance, for n = 4, the alphabet is {a, b, c, d}). For every letter
(call it x), inserting an x in any place in any word has cost I_(x). The
cost to transform a letter x into a letter y is given by
⌈(I_(x) + I_(y))/4⌉, i.e., a fourth part, ceiling, of the sum fo the
insertion costs I_(x) and I_(y).

Input

Input consists of several cases. Each case begins with 2 ≤ n ≤ 26,
followed by n strictly positive natural numbers
$I_{\mbox{\texttt{a}}}, I_{\mbox{\texttt{b}}}, I_{\mbox{\texttt{c}}}, \ldots$.
Follow two words w₁ and w₂ made up of between 1 and 1000 lowercase
letters chosen among the n smallest letters. Assume 1 ≤ I_(x) ≤ 1000 for
every letter x.

Output

For every case, print the minimum cost to make w₁ and w₂ identical.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T11:25:56.761Z

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