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;
}