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

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

int main() {
    string a, b, c;
    cin >> a >> b >> c;

    const int OFS = 50000;
    const int LIM = 2000;
    int alen = a.length();
    int blen = b.length();
    int clen = c.length();
    vector<bool> ab(2 * OFS, true);
    vector<bool> ac(2 * OFS, true);
    vector<bool> bc(2 * OFS, true);
    for (int i = 0; i < alen; i++) {
        for (int j = 0; j < blen; j++) {
            if (!match(a[i], b[j])) ab[i - j + OFS] = false;
        }
    }
    for (int i = 0; i < alen; i++) {
        for (int j = 0; j < clen; j++) {
            if (!match(a[i], c[j])) ac[i - j + OFS] = false;
        }
    }
    for (int i = 0; i < blen; i++) {
        for (int j = 0; j < clen; j++) {
            if (!match(b[i], c[j])) bc[i - j + OFS] = false;
        }
    }

    int ans = 3 * LIM;
    for (int i = -2 * LIM; i <= 2 * LIM; i++) {
        for (int j = -2 * LIM; j <= 2 * LIM; j++) {
            if (ab[i + OFS] && ac[j + OFS] && bc[j - i + OFS]) {
                int l = min({0, i, j});
                int r = max({alen, blen + i, clen + j});
                ans = min(ans, r - l);
            }
        }
    }

    cout << ans << endl;
}
### 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;

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

int main() {
    string a, b, c;
    cin >> a >> b >> c;

    const int OFS = 50000;
    const int LIM = 2000;
    int alen = a.length();
    int blen = b.length();
    int clen = c.length();
    vector<bool> ab(2 * OFS, true);
    vector<bool> ac(2 * OFS, true);
    vector<bool> bc(2 * OFS, true);
    for (int i = 0; i < alen; i++) {
        for (int j = 0; j < blen; j++) {
            if (!match(a[i], b[j])) ab[i - j + OFS] = false;
        }
    }
    for (int i = 0; i < alen; i++) {
        for (int j = 0; j < clen; j++) {
            if (!match(a[i], c[j])) ac[i - j + OFS] = false;
        }
    }
    for (int i = 0; i < blen; i++) {
        for (int j = 0; j < clen; j++) {
            if (!match(b[i], c[j])) bc[i - j + OFS] = false;
        }
    }

    int ans = 3 * LIM;
    for (int i = -2 * LIM; i <= 2 * LIM; i++) {
        for (int j = -2 * LIM; j <= 2 * LIM; j++) {
            if (ab[i + OFS] && ac[j + OFS] && bc[j - i + OFS]) {
                int l = min({0, i, j});
                int r = max({alen, blen + i, clen + j});
                ans = min(ans, r - l);
            }
        }
    }

    cout << ans << endl;
}
```