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;
constexpr int inf32 = 0x3f3f3f3f;
constexpr long long inf64 = 0x3f3f3f3f3f3f3f3f;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vector<int> a(5);
  vector<string> mymap(4);
  for (int i = 1; i <= 4; ++i) cin >> a[i];
  for (int i = (4) - 1; i >= 0; --i) a[i] = min(a[i], a[i + 1]);
  vector<int> g(1 << 16, inf32);
  vector<pair<int, int> > trans;
  g[0] = 0;
  for (int s = 0; s < (1 << 16); ++s)
    if (g[s] != inf32) {
      trans.emplace_back(s, g[s]);
      for (int k = 1; k <= 4; ++k) {
        for (int l = 0; l < (5 - k); ++l) {
          int r = l + k, t = s;
          for (int i = l; i < r; ++i) {
            t = ~(~t | 15 << i * 4);
            t |= max(s >> i * 4 & 15, k) << i * 4;
          }
          g[t] = min(g[t], g[s] + a[k]);
        }
      }
    }
  for (int i = 0; i < (4); ++i) cin >> mymap[i];
  vector<vector<int> > f(n + 1, vector<int>(1 << 8, inf32));
  f[0][0] = 0;
  for (int i = 0; i < (n); ++i) {
    for (int s = 0; s < (1 << 8); ++s)
      if (f[i][s] != inf32) {
        for (pair<int, int> &u : trans) {
          int t = 0;
          for (int j = 0; j < (4); ++j) {
            int len = max(u.first >> j * 4 & 15, s >> j * 2 & 3);
            if (mymap[j][i] == '*' && !len) {
              t = -1;
              break;
            }
            t |= max(len - 1, 0) << j * 2;
          }
          if (!~t) continue;
          f[i + 1][t] = min(f[i + 1][t], f[i][s] + u.second);
        }
      }
  }
  int ns = inf32;
  for (int s = 0; s < (1 << 8); ++s) ns = min(ns, f[n][s]);
  cout << ns << '\n';
  return 0;
}
