In the video game Fallout 4, the quest "Road to Freedom" requires players to reach a metal dial called the "Freedom Trail Ring", and use the dial to spell a specific keyword in order to open the door.

Given a string ring, which represents the code engraved on the outer ring and another string key, which represents the keyword needs to be spelled. You need to find the minimum

1. You can rotate the ring clockwise or anticlockwise one place, which counts as 1 step. The final purpose of the rotation is to align one of the string ring's characters at the 12:00 direction, where this character must equal to the character key[i]
   .
2. If the character key[i] has been aligned at the 12:00 direction, you need to press the center button to spell, which also counts as 1 step. After the pressing, you could begin to spell the next character in the key (next stage), otherwise, you've finished all the spelling.

class Solution {
public:
    int findRotateSteps(string ring, string key) {
        int result[key.length()][ring.length()];
        int answer = INT_MAX;
        for (int i = 0; i < key.length(); i++) {
            for (int j = 0; j < ring.length(); j++) {
                result[i][j] = INT_MAX;
            }
        }
        
        for (int i = 0; i < key.length(); i++) {
             for (int j = 0; j < ring.length(); j++) {
                 if (key[i] == ring[j]) {
                     if (i == 0)
                        result[i][j] = min(abs(i - j), (int)ring.length() - abs(i - j));
                     if (i != 0)
                    for (int k = 0; k < ring.length(); k++) {
                        if (result[i - 1][k] != INT_MAX) {
                            result[i][j] = min(result[i][j], result[i - 1][k] + min(abs(k - j), (int)ring.length() - abs(k - j)));
                            if (i == key.length() - 1 && answer > result[i][j]) {
                                answer = result[i][j];
                            }
                        }
                    }
                 }
             }
        }
        return answer + key.length();
    }
};