Codeforces Round #394 (Div. 2) C. Dasha and Password —— 枚举

题目链接：http://codeforces.com/problemset/problem/761/C

C. Dasha and Password

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Input

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.

Output

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

Examples

input

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

output

1

input

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

output

3

Note

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.

题解：

n<=50，所以即使O（n^3）的复杂度仍绰绰有余。

1.op[i][t]记录：在第i行，跳到类型为t的字符的最少操作数。

2.三个for循环，枚举三种字符所在的行，取最少的操作数之和，即为答案。

代码如下：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const double eps = 1e-6;
const int INF = 2e9;
const LL LNF = 9e18;
const int mod = 1e9+7;
const int maxn = 50*50+10;

int n,m, op[55][4];
char s[100];

int main()
{
    cin>>n>>m;
    for(int i = 1; i<=n; i++)   //初始化操作次数为无限大
    for(int j = 1; j<=3; j++)
        op[i][j] = INF/3;

    for(int i = 1; i<=n; i++)
    {
        scanf("%s",s);
        for(int j = 0; j<m; j++)
        {
            int t;  //t为type， 即字符的类型
            if(s[j]=='#' ||s[j]=='*' || s[j]=='&')
                t = 1;
            else if(s[j]>='a' && s[j]<='z')
                t = 2;
            else
                t = 3;
            op[i][t] = min(op[i][t], min(j,m-j));   //左右两个方向的移动都需考虑
        }
    }

    int ans = INF;
    for(int i = 1; i<=n; i++)   //枚举" # * & "所在的行
    {
        for(int j = 1; j<=n; j++)   //枚举abcd……所在的行
        {
            if(i==j) continue;
            for(int k = 1; k<=n; k++)   //枚举123……所在的行
            {
                if(k==i || k==j) continue;
                ans = min(ans, op[i][1]+op[j][2]+op[k][3]); //操作次数之和
            }
        }
    }
    cout<<ans<<endl;
}