Dasha and Password

### 题目描述 克服了上楼的困难后，Dasha走进了教室，在上课之前，Dasha需要写下一串密码。密码由满足如下性质的长度为$n$的字符串组成： * 字符串中至少有一个字符为'0'-'9'的数码。 * 字符串中至少有一个字符为小写拉丁字母（'a'-'z'）。 * 字符串中至少有一个字符为'#', '*', '&'三个字符中的一个。 给定$n$个字符串，每个字符串长度为$m$，**密码将由这$n$个字符串中每个字符串贡献一个字符组成**。 对于每个字符串，都有一个指针指向某个下标。初始时，每个字符串的指针都指向这个字符串的第一个字符，**最终的密码将由这些指针指向的字符拼接而成**。 每操作一次，都可以将这个指针向左或是向右移动一位。**且这个字符串是环形的**，即如果当前指针指向第一个字符，那么向左移动一位后它将指向第$m$个字符；如果当前指针指向第$m$个字符，那么向右移动一位后它将指向第一个字符。 求最少需要几次操作可以获得符合要求的密码。

After overcoming the stairs Dasha came to classes. She needed to write a password to begin her classes. The password is a string of length $ n $ which satisfies the following requirements: - There is at least one digit in the string, - There is at least one lowercase (small) letter of the Latin alphabet in the string, - There is at least one of three listed symbols in the string: '\#', '\*', '&'. Considering that these are programming classes it is not easy to write the password. For each character of the password we have a fixed string of length $ m $ , on each of these $ n $ strings there is a pointer on some character. The $ i $ -th character displayed on the screen is the pointed character in the $ i $ -th string. Initially, all pointers are on characters with indexes $ 1 $ in the corresponding strings (all positions are numbered starting from one). During one operation Dasha can move a pointer in one string one character to the left or to the right. Strings are cyclic, it means that when we move the pointer which is on the character with index $ 1 $ to the left, it moves to the character with the index $ m $ , and when we move it to the right from the position $ m $ it moves to the position $ 1 $ . You need to determine the minimum number of operations necessary to make the string displayed on the screen a valid password.

The first line contains two integers $ n $ , $ m $ $ (3<=n<=50,1<=m<=50) $ — the length of the password and the length of strings which are assigned to password symbols. Each of the next $ n $ lines contains the string which is assigned to the $ i $ -th symbol of the password string. Its length is $ m $ , it consists of digits, lowercase English letters, and characters '\#', '\*' or '&'. You have such input data that you can always get a valid password.

Print one integer — the minimum number of operations which is necessary to make the string, which is displayed on the screen, a valid password.

3 4
1**2
a3*0
c4**

1

5 5
#*&#*
*a1c&
&q2w*
#a3c#
*&#*&

3

In the first test it is necessary to move the pointer of the third string to one left to get the optimal answer. In the second test one of possible algorithms will be: - to move the pointer of the second symbol once to the right. - to move the pointer of the third symbol twice to the right.