#include <iostream>
#include <string>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define m 2000

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

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

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

    int al = a.length();
    int bl = b.length();
    int cl = c.length();
    
    rep(i, al)
    {
        rep(j, bl)
        {
            if (!match(a[i], b[j]))
                ab[i - j + 50000] = true;
        }
    }
    rep(i, al)
    {
        rep(j, cl)
        {
            if (!match(a[i], c[j]))
                ac[i - j + 50000] = true;
        }
    }
    rep(i, bl)
    {
        rep(j, cl)
        {
            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(al, max(bl + i, cl + j));
                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 <iostream>
#include <string>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define m 2000

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

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

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

    int al = a.length();
    int bl = b.length();
    int cl = c.length();
    
    rep(i, al)
    {
        rep(j, bl)
        {
            if (!match(a[i], b[j]))
                ab[i - j + 50000] = true;
        }
    }
    rep(i, al)
    {
        rep(j, cl)
        {
            if (!match(a[i], c[j]))
                ac[i - j + 50000] = true;
        }
    }
    rep(i, bl)
    {
        rep(j, cl)
        {
            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(al, max(bl + i, cl + j));
                ans = min(ans, r - l);
            }
        }
    }

    cout << ans << endl;

    return 0;
}
```