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;
int a[4];
char c[4][1001];
int d[1001 + 100][1 << 12];
inline int getind(int i, int j) { return i * 4 + j; }
inline int get(int mask, int i, int j) { return (mask >> getind(i, j)) & 1; }
void go(int i, int mask, int nmask, int val, int j = 0) {
  if (j == 4) {
    if (d[i + 1][nmask >> 4] == -1 || d[i + 1][nmask >> 4] > val) {
      d[i + 1][nmask >> 4] = val;
    }
    return;
  }
  if (c[j][i] == '.' || get(nmask, 0, j)) {
    go(i, mask, nmask, val, j + 1);
  }
  if (j <= 0) {
    go(i, mask, nmask | ((1 << 16) - 1), val + a[3], j + 1);
  }
  if (j <= 1) {
    int t = 0;
    for (int x = 0; x < 3; ++x)
      for (int y = 0; y < 3; ++y) t |= (1 << getind(x, j + y));
    go(i, mask, nmask | t, val + a[2], j + 1);
  }
  if (j <= 2) {
    int t = 0;
    for (int x = 0; x < 2; ++x)
      for (int y = 0; y < 2; ++y) t |= (1 << getind(x, j + y));
    go(i, mask, nmask | t, val + a[1], j + 1);
  }
  go(i, mask, nmask | (1 << getind(0, j)), val + a[0], j + 1);
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < 4; ++i) scanf("%d", &a[i]);
  for (int i = 0; i < 4; ++i) {
    scanf("%s", c[i]);
  }
  memset(d, -1, sizeof(d));
  d[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int mask = 0; mask < (1 << 12); ++mask) {
      if (d[i][mask] == -1) continue;
      go(i, mask, mask, d[i][mask]);
    }
  }
  printf("%d\n", d[n][0]);
  return 0;
}
