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

const int MX = 2005;
bool d[3][3][MX];

int main() {
  vector<string> s(3);
  rep(i,3) cin >> s[i];
  sort(s.begin(),s.end());
  int ans = MX*3;
  do {
    memset(d, false, sizeof(d));
    rep(i,3)rep(j,3)rep(k,s[i].size()) {
      if (i >= j) continue;
      bool ok = true;
      for (int ni = k; ni < s[i].size(); ni++) {
        int nj = ni-k;
        if (nj >= s[j].size()) break;
        if (s[i][ni] == '?' || s[j][nj] == '?') continue;
        if (s[i][ni] != s[j][nj]) ok = false;
      }
      d[i][j][k] = ok;
    }

    auto f = [&](int i, int j, int k) {
      if (k >= s[i].size()) return true;
      return d[i][j][k];
    };

    rep(x,MX)rep(y,MX) {
      if (!f(0,1,x)) continue;
      if (!f(1,2,y)) continue;
      if (!f(0,2,x+y)) continue;
      int now = 0;
      now = max<int>(now, s[0].size());
      now = max<int>(now, x+s[1].size());
      now = max<int>(now, x+y+s[2].size());
      ans = min(ans, now);
    }
  } while (next_permutation(s.begin(), s.end()));
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

const int MX = 2005;
bool d[3][3][MX];

int main() {
  vector<string> s(3);
  rep(i,3) cin >> s[i];
  sort(s.begin(),s.end());
  int ans = MX*3;
  do {
    memset(d, false, sizeof(d));
    rep(i,3)rep(j,3)rep(k,s[i].size()) {
      if (i >= j) continue;
      bool ok = true;
      for (int ni = k; ni < s[i].size(); ni++) {
        int nj = ni-k;
        if (nj >= s[j].size()) break;
        if (s[i][ni] == '?' || s[j][nj] == '?') continue;
        if (s[i][ni] != s[j][nj]) ok = false;
      }
      d[i][j][k] = ok;
    }

    auto f = [&](int i, int j, int k) {
      if (k >= s[i].size()) return true;
      return d[i][j][k];
    };

    rep(x,MX)rep(y,MX) {
      if (!f(0,1,x)) continue;
      if (!f(1,2,y)) continue;
      if (!f(0,2,x+y)) continue;
      int now = 0;
      now = max<int>(now, s[0].size());
      now = max<int>(now, x+s[1].size());
      now = max<int>(now, x+y+s[2].size());
      ans = min(ans, now);
    }
  } while (next_permutation(s.begin(), s.end()));
  cout << ans << endl;
  return 0;
}

```