#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> P;
typedef long long ll;
typedef long double ld;
const int inf=1e9+7;
const ll longinf=1LL<<60;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
#define F first
#define S second

const int mx=100010;
const ll mod=1e9+7;

const int m=2000;

bool ch(char a, char b){ return (a==b || a=='?' || b=='?'); }

int main() {
  string a,b,c;
  cin >> a >> b >> c;
  int az = a.size();
  int bz = b.size();
  int cz = c.size();
  vector<bool> ab(mx,true),ac(mx,true),bc(mx,true);
  rep(i,az)rep(j,bz)if(!ch(a[i],b[j])) ab[i-j+50000] = false;
  rep(i,az)rep(j,cz)if(!ch(a[i],c[j])) ac[i-j+50000] = false;
  rep(i,bz)rep(j,cz)if(!ch(b[i],c[j])) bc[i-j+50000] = false;

  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+50000] && ac[j+50000] && bc[j-i+50000]){
      int l = min(0,min(i,j));
      int r = max(az,max(bz+i,cz+j));
      ans = min(ans, r-l);
    }
  }
  cout << ans << endl;
  return 0;
}
### Prompt

Your task is to create a Cpp solution to the following problem:

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.

Examples

Input

a?c
der
cod


Output

7


Input

atcoder
atcoder
???????


Output

7

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> P;
typedef long long ll;
typedef long double ld;
const int inf=1e9+7;
const ll longinf=1LL<<60;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
#define F first
#define S second

const int mx=100010;
const ll mod=1e9+7;

const int m=2000;

bool ch(char a, char b){ return (a==b || a=='?' || b=='?'); }

int main() {
  string a,b,c;
  cin >> a >> b >> c;
  int az = a.size();
  int bz = b.size();
  int cz = c.size();
  vector<bool> ab(mx,true),ac(mx,true),bc(mx,true);
  rep(i,az)rep(j,bz)if(!ch(a[i],b[j])) ab[i-j+50000] = false;
  rep(i,az)rep(j,cz)if(!ch(a[i],c[j])) ac[i-j+50000] = false;
  rep(i,bz)rep(j,cz)if(!ch(b[i],c[j])) bc[i-j+50000] = false;

  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+50000] && ac[j+50000] && bc[j-i+50000]){
      int l = min(0,min(i,j));
      int r = max(az,max(bz+i,cz+j));
      ans = min(ans, r-l);
    }
  }
  cout << ans << endl;
  return 0;
}
```