#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i=0; i<(int)(n); ++i)

const int MX = 2000;
bool ab[20000], ac[20000], bc[20000]; // where not match

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

int main () {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  
  string a, b, c;
  cin >> a >> b >> c;
  int la = a.length();
  int lb = b.length();
  int lc = c.length();
  
  rep(i, la) rep(j, lb) if(!match(a[i], b[j])) ab[10000-j+i] = true;
  rep(i, la) rep(j, lc) if(!match(a[i], c[j])) ac[10000-j+i] = true;
  rep(i, lb) rep(j, lc) if(!match(b[i], c[j])) bc[10000-j+i] = true;
  
  int ans = 3*MX;
  for (int i=-2*MX; i<=2*MX; ++i) {
    for (int j=-2*MX; j<=2*MX; ++j) {
      if (!ab[i+10000] && !ac[j+10000] && !bc[10000-i+j]) {
        int L = min(0, min(i, j));
        int R = max(la, max(lb+i, lc+j));
        ans = min(ans, R-L);
      }
    }
  }
  cout << ans << endl;
}
### Prompt

Develop a solution in CPP to the problem described below:

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

const int MX = 2000;
bool ab[20000], ac[20000], bc[20000]; // where not match

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

int main () {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  
  string a, b, c;
  cin >> a >> b >> c;
  int la = a.length();
  int lb = b.length();
  int lc = c.length();
  
  rep(i, la) rep(j, lb) if(!match(a[i], b[j])) ab[10000-j+i] = true;
  rep(i, la) rep(j, lc) if(!match(a[i], c[j])) ac[10000-j+i] = true;
  rep(i, lb) rep(j, lc) if(!match(b[i], c[j])) bc[10000-j+i] = true;
  
  int ans = 3*MX;
  for (int i=-2*MX; i<=2*MX; ++i) {
    for (int j=-2*MX; j<=2*MX; ++j) {
      if (!ab[i+10000] && !ac[j+10000] && !bc[10000-i+j]) {
        int L = min(0, min(i, j));
        int R = max(la, max(lb+i, lc+j));
        ans = min(ans, R-L);
      }
    }
  }
  cout << ans << endl;
}
```