#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;

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

    int A = a.length();
    int B = b.length();
    int C = c.length();

    bool ab[8001], ac[8001], bc[16001];
    for (int i = 0; i <= 8000; i++) {
        ab[i] = ac[i] = true;
    }
    for (int i = 0; i <= 16000; i++) bc[i] = true;
    
    for (int i = -B + 1; i < A; i++) {
        for (int j = max(0, i); j < min(A, i + B); j++) {
            if (a[j] != '?' && b[j - i] != '?' && a[j] != b[j - i]) ab[i + 4000] = false;
        }
    }
    for (int i = -C + 1; i < A; i++) {
        for (int j = max(0, i); j < min(A, i + C); j++) {
            if (a[j] != '?' && c[j - i] != '?' && a[j] != c[j - i]) ac[i + 4000] = false;
        }
    }
    for (int i = -C + 1; i < B; i++) {
        for (int j = max(0, i); j < min(B, i + C); j++) {
            if (b[j] != '?' && c[j - i] != '?' && b[j] != c[j - i]) bc[i + 8000] = false;
        }
    }

    int ans = 10000;
    for (int i = -4000; i <= 4000; i++) for (int j = -4000; j <= 4000; j++) {
        if (ab[i + 4000] && ac[j + 4000] && bc[j - i + 8000]) {
            int l = min(0, min(i, j));
            int r = max(A, max(i + B, j + C));
            ans = min(ans, r - l);
        }
    }

    cout << ans << endl;
    return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
typedef long long ll;
typedef pair<int, int> pii;

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

    int A = a.length();
    int B = b.length();
    int C = c.length();

    bool ab[8001], ac[8001], bc[16001];
    for (int i = 0; i <= 8000; i++) {
        ab[i] = ac[i] = true;
    }
    for (int i = 0; i <= 16000; i++) bc[i] = true;
    
    for (int i = -B + 1; i < A; i++) {
        for (int j = max(0, i); j < min(A, i + B); j++) {
            if (a[j] != '?' && b[j - i] != '?' && a[j] != b[j - i]) ab[i + 4000] = false;
        }
    }
    for (int i = -C + 1; i < A; i++) {
        for (int j = max(0, i); j < min(A, i + C); j++) {
            if (a[j] != '?' && c[j - i] != '?' && a[j] != c[j - i]) ac[i + 4000] = false;
        }
    }
    for (int i = -C + 1; i < B; i++) {
        for (int j = max(0, i); j < min(B, i + C); j++) {
            if (b[j] != '?' && c[j - i] != '?' && b[j] != c[j - i]) bc[i + 8000] = false;
        }
    }

    int ans = 10000;
    for (int i = -4000; i <= 4000; i++) for (int j = -4000; j <= 4000; j++) {
        if (ab[i + 4000] && ac[j + 4000] && bc[j - i + 8000]) {
            int l = min(0, min(i, j));
            int r = max(A, max(i + B, j + C));
            ans = min(ans, r - l);
        }
    }

    cout << ans << endl;
    return 0;
}
```