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 *a*<sub class="lower-index">*k*</sub> coins.

What is the minimum number of coins you have to pay to replace all asterisks with dots?
The first line contains one integer *n* (4 ≤ *n* ≤ 1000) — the number of columns in *f*.

The second line contains 4 integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>, *a*<sub class="lower-index">4</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 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.
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.
4
1 10 8 20
***.
***.
***.
...*
9
7
2 1 8 2
.***...
.***..*
.***...
....*..
3
4
10 10 1 10
***.
*..*
*..*
.***
2
5
4 3 4 4
.....
****.
..***
...**
7
6
15 3 18 16
.*.***
...**.
*.....
**..*.
15
5
2 1 2 1
*.***
***.*
.*..*
***..
2
4
2 23 19 1
..**
*...
**.*
.*.*
1
4
18 17 3 15
**..
***.
*..*
****
9
4
13 12 20 12
**.*
....
***.
*.**
12
6
8 2 11 9
.*.***
..**.*
.**.**
*.****
12
6
1 2 2 1
...*.*
.**...
*.*.*.
**...*
2
6
2 2 2 1
*.****
.*....
.*.***
*.***.
2
5
9 19 10 7
.....
*.*.*
.*.**
..**.
14
10
1 1 1 1
.**.*.****
.*.**..***
.*...*..**
*.*.**..*.
3
4
1 1 1 1
****
****
****
****
1
10
433 514 452 478
**********
**********
**********
**********
1434
4
1000 1000 1000 1000
****
****
****
****
1000
4
1 4 9 16
****
**.*
*.**
..**
12
4
1 4 9 15
****
****
****
****
15
33
548 102 31 730
.**..**.**...******.*.**....**.**
**..******...*.*...*.....*....*.*
.**..*...*.**.*.....*..*..**.*..*
.....**.....*..*...***.***..**.**
527
print("_RANDOM_GUESS_1692479286.9532456")# 1692479286.953265