Problem:
Score : 500 points

Problem Statement

Snuke has a string s.
From this string, Anuke, Bnuke, and Cnuke obtained strings a, b, and c, respectively, as follows:

Choose a non-empty (contiguous) substring of s (possibly s itself). Then, replace some characters (possibly all or none) in it with ?s.

For example, if s is mississippi, we can choose the substring ssissip and replace its 1-st and 3-rd characters with ? to obtain ?s?ssip.

You are given the strings a, b, and c.
Find the minimum possible length of s.

Constraints

1 \leq |a|, |b|, |c| \leq 2000

a, b, and c consists of lowercase English letters and ?s.

Input

Input is given from Standard Input in the following format:

a
b
c

Output

Print the minimum possible length of s.

Sample Input 1

a?c
der
cod

Sample Output 1

7

For example, s could be atcoder.

Sample Input 2

atcoder
atcoder
???????

Sample Output 2

7

a, b, and c may not be distinct.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

import static java.lang.Integer.max;
import static java.lang.Integer.min;

public class Main {
    private static final int M = 2000;
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        char[] a = scanner.nextLine().toCharArray();
        char[] b = scanner.nextLine().toCharArray();
        char[] c = scanner.nextLine().toCharArray();
        boolean[] ab = new boolean[10*M];
        boolean[] ac = new boolean[10*M];
        boolean[] bc = new boolean[10*M];

        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < b.length; j++) {
                if(!match(a[i], b[j])) ab[i-j+5*M] = true;
            }
        }
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < c.length; j++) {
                if(!match(a[i], c[j])) ac[i-j+5*M] = true;
            }
        }
        for (int i = 0; i < b.length; i++) {
            for (int j = 0; j < c.length; j++) {
                if(!match(b[i], c[j])) bc[i-j+5*M] = true;
            }
        }
        int ans = 3*M;
        for (int i = -2*M; i <= 2*M ; i++) {
            for (int j = -2*M; j <= 2*M ; j++) {
                if(!ab[i+5*M] && !ac[j+5*M] && !bc[j-i+5*M]){
                    int L = min(0, min(i,j));
                    int R = max(a.length, max(b.length + i, c.length +j));
                    ans = min(ans,R-L);
                }
            }
        }
        System.out.println(ans);
    }

    private static boolean match(char c1, char c2){
        return c1 == '?' || c2 == '?' || c1 == c2;
    }
}