#include <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iomanip>

using namespace std;

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

#define M 2000

bool ab[100000], ac[100000], bc[100000];

string a, b, c;

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

int main()
{
  cin >> a >> b >> c;
  int A = a.length(), B = b.length(), C = c.length();
  int i, j;
  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 (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(A, max(B + i, C + j));
        ans = min(ans, R - L);
      }
    }
  }

  cout << ans << endl;
}

### 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 <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iomanip>

using namespace std;

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

#define M 2000

bool ab[100000], ac[100000], bc[100000];

string a, b, c;

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

int main()
{
  cin >> a >> b >> c;
  int A = a.length(), B = b.length(), C = c.length();
  int i, j;
  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 (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(A, max(B + i, C + j));
        ans = min(ans, R - L);
      }
    }
  }

  cout << ans << endl;
}

```