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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <string>

using namespace std;

#define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)

#define M 2000

bool ab[100000],ac[100000],bc[100000];

bool match(char c1, char c2){
return (c1 == '?' || c2 == '?' || c1 == c2);
}

int main(void){
int i,j;

string a,b,c;
cin >> a >> b >> c;

int A = a.length();
int B = b.length();
int C = c.length();

REP(i,A) REP(j,B) if(!match(a[i], b[j])) ab[i-j+50000] = true;
REP(i,A) REP(j,C) if(!match(a[i], c[j])) ac[i-j+50000] = true;
REP(i,B) REP(j,C) if(!match(b[i], c[j])) bc[i-j+50000] = true;

int ans = 3 * M;
for(i=-2*M;i<=2*M;i++) for(j=-2*M;j<=2*M;j++) if(!ab[i+50000] && !ac[j+50000] && !bc[j-i+50000]){
int L = min(0, min(i, j));
int R = max(A, max(B + i, C + j));
ans = min(ans, R - L);
}

cout << ans << endl;

return 0;
}