#include <iostream>
#include <string>
#include <vector>

using namespace std;

constexpr int M = 2000;
bool match(char a, char b) { return a == b || a == '?' || b == '?'; }

int main() {
  string a, b, c;
  cin >> a >> b >> c;
  vector<bool> ab(100000, false);
  vector<bool> ac(100000, false);
  vector<bool> bc(100000, false);
  // それぞれがいくつずれたときに成立するか
  int A = a.length();
  int B = b.length();
  int C = c.length();
  for (int i = 0; i < A; i++)
    for (int j = 0; j < B; j++)
      if (!match(a[i], b[j]))
        ab[i - j + 50000] = true;
  for (int i = 0; i < A; i++)
    for (int j = 0; j < C; j++)
      if (!match(a[i], c[j]))
        ac[i - j + 50000] = true;
  for (int i = 0; i < B; i++)
    for (int j = 0; j < C; j++)
      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 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 <iostream>
#include <string>
#include <vector>

using namespace std;

constexpr int M = 2000;
bool match(char a, char b) { return a == b || a == '?' || b == '?'; }

int main() {
  string a, b, c;
  cin >> a >> b >> c;
  vector<bool> ab(100000, false);
  vector<bool> ac(100000, false);
  vector<bool> bc(100000, false);
  // それぞれがいくつずれたときに成立するか
  int A = a.length();
  int B = b.length();
  int C = c.length();
  for (int i = 0; i < A; i++)
    for (int j = 0; j < B; j++)
      if (!match(a[i], b[j]))
        ab[i - j + 50000] = true;
  for (int i = 0; i < A; i++)
    for (int j = 0; j < C; j++)
      if (!match(a[i], c[j]))
        ac[i - j + 50000] = true;
  for (int i = 0; i < B; i++)
    for (int j = 0; j < C; j++)
      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;
}

```