Clear The Matrix

Description:

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 ≤ 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.

Output:

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

Sample Input:

4
1 10 8 20
***.
***.
***.
...*

Sample Output:

9

Sample Input:

7
2 1 8 2
.***...
.***..*
.***...
....*..

Sample Output:

3

Sample Input:

4
10 10 1 10
***.
*..*
*..*
.***

Sample Output:

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.