#include <bits/stdc++.h>
using namespace std;

int main() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);

  string a, b, c;
  cin >> a >> b >> c;
  
  const int s = 2000, N = 5e4;
  int na = a.size(), nb = b.size(), nc = c.size();
  vector<bool> ab(2 * N, 1), bc(2 * N, 1), ac(2 * N, 1);

  auto match = [&](char l, char r) {
    return (l == r || l == '?' || r == '?');
  };

  for (int i = 0; i < na; ++i) {
    for (int j = 0; j < nb; ++j) {
      if (!match(a[i], b[j])) ab[i - j + N] = 0;
    }
  }

  for (int i = 0; i < na; ++i) {
    for (int j = 0; j < nc; ++j) {
      if (!match(a[i], c[j])) ac[i - j + N] = 0;
    }
  }

  for (int i = 0; i < nb; ++i) {
    for (int j = 0; j < nc; ++j) {
      if (!match(b[i], c[j])) bc[i - j + N] = 0;
    }
  }

  int ans = 3 * s;
  for (int i = -2*s; i <= 2*s; ++i) {
    for (int j = -2*s; j <= 2*s; ++j) {
      if (ab[i + N] && ac[j + N] && bc[j-i+N]) {
        int l = min({0, i, j});
        int r = max({na, i + nb, j + nc});
        ans = min(ans, r - l);
      }
    }
  }

  cout << ans << '\n';
}

### Prompt

Please create a solution in Cpp 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;

int main() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);

  string a, b, c;
  cin >> a >> b >> c;
  
  const int s = 2000, N = 5e4;
  int na = a.size(), nb = b.size(), nc = c.size();
  vector<bool> ab(2 * N, 1), bc(2 * N, 1), ac(2 * N, 1);

  auto match = [&](char l, char r) {
    return (l == r || l == '?' || r == '?');
  };

  for (int i = 0; i < na; ++i) {
    for (int j = 0; j < nb; ++j) {
      if (!match(a[i], b[j])) ab[i - j + N] = 0;
    }
  }

  for (int i = 0; i < na; ++i) {
    for (int j = 0; j < nc; ++j) {
      if (!match(a[i], c[j])) ac[i - j + N] = 0;
    }
  }

  for (int i = 0; i < nb; ++i) {
    for (int j = 0; j < nc; ++j) {
      if (!match(b[i], c[j])) bc[i - j + N] = 0;
    }
  }

  int ans = 3 * s;
  for (int i = -2*s; i <= 2*s; ++i) {
    for (int j = -2*s; j <= 2*s; ++j) {
      if (ab[i + N] && ac[j + N] && bc[j-i+N]) {
        int l = min({0, i, j});
        int r = max({na, i + nb, j + nc});
        ans = min(ans, r - l);
      }
    }
  }

  cout << ans << '\n';
}

```