A11560. Clear The Matrix

You are given a matrix $f$ with $4$ rows and $n$ columns. Each element of the matrix is either an asterisk (\*) or a dot (.).

You may perform the following operation arbitrary number of times: choose a square submatrix of $f$ with size $k×k$ (where $1<=k<=4$ ) and replace each element of the chosen submatrix with a dot. Choosing a submatrix of size $k×k$ costs $a_{k}$ coins.

What is the minimum number of coins you have to pay to replace all asterisks with dots?

The first line contains one integer $n$ ( $4<=n<=1000$ ) — the number of columns in $f$ .

The second line contains $4$ integers $a_{1}$ , $a_{2}$ , $a_{3}$ , $a_{4}$ ( $1<=a_{i}<=1000$ ) — the cost to replace the square submatrix of size $1×1$ , $2×2$ , $3×3$ or $4×4$ , respectively.

Then four lines follow, each containing $n$ characters and denoting a row of matrix $f$ . Each character is either a dot or an asterisk.

Print one integer — the minimum number of coins to replace all asterisks with dots.

In the first example you can spend $8$ coins to replace the submatrix $3×3$ in the top-left corner, and $1$ coin to replace the $1×1$ submatrix in the bottom-right corner.

In the second example the best option is to replace the $4×4$ submatrix containing columns $2–5$ , and the $2×2$ submatrix consisting of rows $2–3$ and columns $6–7$ .

In the third example you can select submatrix $3×3$ in the top-left corner and then submatrix $3×3$ consisting of rows $2–4$ and columns $2–4$ .