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.
#include <bits/stdc++.h>
using namespace std;
int n, cost[5], dp[4][1000][1 << 12];
char g[4][1001];
int who[4][4], col[1000];
int calc(int r, int c, int mask) {
  if (r == 4) {
    if (col[c] & ~mask) return 1e9;
    return calc(0, c + 1, mask >> 4);
  }
  if (c == n) return 0;
  int &ret = dp[r][c][mask];
  if (ret != -1) return ret;
  ret = calc(r + 1, c, mask);
  for (int s = 1; s <= 4 && r + s <= 4 && c + s <= n; ++s) {
    if (s == 4)
      ret = min(ret, cost[s] + calc(0, c + 1, (1 << 12) - 1));
    else
      ret = min(ret, cost[s] + calc(r + 1, c, mask | who[r][s]));
  }
  return ret;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; ++i) scanf("%d", cost + i);
  for (int i = 0; i < 4; ++i) {
    for (int s = 1; s < 4 && i + s <= 4; ++s) {
      for (int dr = 0; dr < s; ++dr)
        for (int dc = 0; dc < s; ++dc) {
          int r = i + dr;
          int c = dc;
          who[i][s] |= 1 << (c * 4 + r);
        }
    }
  }
  for (int i = 0; i < 4; ++i) {
    scanf("%s", g[i]);
    for (int j = 0; j < n; ++j)
      if (g[i][j] == '*') col[j] |= 1 << i;
  }
  memset(dp, -1, sizeof(dp));
  printf("%d\n", calc(0, 0, 0));
  return 0;
}
