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?

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.

Examples

Input

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


Output

9


Input

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


Output

3


Input

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


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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author darkhan imangaliyev
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyReader in = new MyReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        final static int oo = Integer.MAX_VALUE / 2;
        int[] cost;
        int[] ms;
        int[] b;
        int[][] dp;

        public void solve(int testNumber, MyReader in, PrintWriter out) {
            int n = in.nextInt();
            cost = new int[4];
            for (int i = 0; i < 4; ++i) {
                cost[i] = in.nextInt();
            }
            ms = new int[4];
            for (int i = 0; i < 4; ++i) {
                ms[i] = (1 << (i + 1)) - 1; //1 << (i + 1) - 1 != (1 << (i + 1)) - 1; 2 ^ (i+1) - 1 vs 2 ^ (i + 1 - 1)
            }
            char[][] c = new char[4][n];
            for (int i = 0; i < 4; ++i) {
                c[i] = in.next().toCharArray();
            }
            b = new int[n];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < 4; ++j) {
                    if (c[j][i] == '*') {
                        b[i] |= 1 << j;
                    }
                }
            }

            dp = new int[n + 1][1 << 12];
            for (int[] i : dp) {
                Arrays.fill(i, oo);
            }
            int msk = b[0] + (b[1] << 4) + (b[2] << 8);
            dp[0][msk] = 0;
            for (int i = 0; i < n; ++i) {
                for (int mask = (1 << 12) - 1; mask >= 0; --mask) {
                    if (dp[i][mask] == oo) {
                        continue;
                    }
                    if (mask % 16 == 0) {
                        int nmask = mask >> 4;
                        if (i + 3 < n) {
                            nmask += (b[i + 3] << 8);
                        }
                        dp[i + 1][nmask] = Math.min(dp[i + 1][nmask], dp[i][mask]);
                    }
                    dp[i + 1][0] = Math.min(dp[i + 1][0], dp[i][mask] + cost[3]);
                    for (int k = 0; k < 3; ++k) {
                        for (int z = 0; z + k < 4; ++z) {
                            int nmask = mask;
                            for (int p = 0; p <= k; ++p) {
                                nmask &= ~(ms[k] << (4 * p + z));
                            }
                            dp[i][nmask] = Math.min(dp[i][nmask], dp[i][mask] + cost[k]);
                        }
                    }
                }
            }
            out.println(dp[n - 1][0]);
        }

    }

    static class MyReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public MyReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

