Clear The Matrix
Description
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 ak 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 a1, a2, a3, a4 (1 ≤ ai ≤ 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.
Input
The first line contains one integer n (4 ≤ n ≤ 1000) — the number of columns in f.
The second line contains 4 integers a1, a2, a3, a4 (1 ≤ ai ≤ 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.
Output
Print one integer — the minimum number of coins to replace all asterisks with dots.
Samples
4
1 10 8 20
***.
***.
***.
...*
9
7
2 1 8 2
.***...
.***..*
.***...
....*..
3
4
10 10 1 10
***.
*..*
*..*
.***
2
Note
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.