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

using i64 = int64_t;

constexpr int N = 2000;
constexpr int M = 20000;

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

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

    vector<bool> ab(M), bc(M), ac(M);
    for(int i=0;i<a.size();++i){
        for(int j=0;j<b.size();++j){
            if(!match(a[i], b[j]))ab[i-j+M/2] = true;
        }
    }
    for(int i=0;i<a.size();++i){
        for(int j=0;j<c.size();++j){
            if(!match(a[i], c[j]))ac[i-j+M/2] = true;
        }
    }
    for(int i=0;i<b.size();++i){
        for(int j=0;j<c.size();++j){
            if(!match(b[i], c[j]))bc[i-j+M/2] = true;
        }
    }

    int ans = 3*N;
    for(int i=-2*N;i<=2*N;++i){
        for(int j=-2*N;j<=2*N;++j){
            if(!ab[i+M/2] && !ac[j+M/2] && !bc[j-i+M/2]){
                int left = min({0, i, j});
                int right = max({(int)a.size(), i+(int)b.size(), j+(int)c.size()});
                ans = min(ans, right - left);
            }
        }
    }

    cout << ans << endl;

    return 0;
}
### 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;

using i64 = int64_t;

constexpr int N = 2000;
constexpr int M = 20000;

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

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

    vector<bool> ab(M), bc(M), ac(M);
    for(int i=0;i<a.size();++i){
        for(int j=0;j<b.size();++j){
            if(!match(a[i], b[j]))ab[i-j+M/2] = true;
        }
    }
    for(int i=0;i<a.size();++i){
        for(int j=0;j<c.size();++j){
            if(!match(a[i], c[j]))ac[i-j+M/2] = true;
        }
    }
    for(int i=0;i<b.size();++i){
        for(int j=0;j<c.size();++j){
            if(!match(b[i], c[j]))bc[i-j+M/2] = true;
        }
    }

    int ans = 3*N;
    for(int i=-2*N;i<=2*N;++i){
        for(int j=-2*N;j<=2*N;++j){
            if(!ab[i+M/2] && !ac[j+M/2] && !bc[j-i+M/2]){
                int left = min({0, i, j});
                int right = max({(int)a.size(), i+(int)b.size(), j+(int)c.size()});
                ans = min(ans, right - left);
            }
        }
    }

    cout << ans << endl;

    return 0;
}
```