Antipalindrome

Consider an alphabet consisting of lowercase and uppercase English letters. Let's enumerate the letters of the alphabet in such a way that lowercase letters have numbers from $1$ to $26$ (in alphabetical order) and uppercase letters have numbers from $27$ to $52$ (also in alphabetical order). For example, symbol $b$ has number $2$, symbol $Y$ has number $51$.

You are given a string $s$ consists of the first $k$ symbols of alphabet. You are also given a matrix $C$ of size $k \times k$, consisting of non-negative integers. The element $C\_{ij}$ denotes the cost to change the symbol number $i$ to the symbol number $j$ at some position of the string $s$. It's guaranteed that $C\_{ii} = 0$.

You should change some symbols of the string $s$ in such a way that $s$ will not contain any palindrome substring of length more than $1$. Also, find the cheapest way to do that.

Note the changes of the symbol number $i$ to the symbol number $j$ at different positions are counted separately. Note also that you can change the symbol at each position not more than once.

The first line contains one integer $k$ ($1 \le k \le 52$) --- the size of the alphabet.

The second line contains a string $s$ ($1 \le |s| \le 5 \cdot 10^6$) constisting of only lowercase and uppercase English letters with numbers not greater than $k$.

The $i$-th of the next $k$ lines contains $k$ integers $C\_{ij}$ ($0 \le C\_{ij} \le 10^9$) --- the cost to change the symbol number $i$ to the symbol number $j$.

Note that the length of the string $s$ may be quite large, so use fast methods to read it (for example function scanf in C++ language and BufferedReader class in Java language).

If it is possible to get a string without palindrome substrings of length more than $1$ print the single integer $c$ --- the minimum cost to obtain such a string. Otherwise print the only integer "-1" (without quotes).