#include <bits/stdc++.h>
#define REP(i,n) for(int (i)=0;(i)<(int)(n);(i)++)
using namespace std;

const int N=2000;
bool ab[100000], ac[100000], bc[100000];

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

int main() {
    string a,b,c;
    cin >> a >> b >> c;
    int A=a.length();
    int B=b.length();
    int C=c.length();

    REP(i,A) REP(j,B) if(!match(a[i], b[j])) ab[i-j+50000]=true;
    REP(i,A) REP(j,C) if(!match(a[i], c[j])) ac[i-j+50000]=true;
    REP(i,B) REP(j,C) if(!match(b[i], c[j])) bc[i-j+50000]=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+50000] && !ac[j+50000] && !bc[j-i+50000]) {
                int l=min({0, i, j});
                int r=max({A, B+i, C+j});
                ans=min(ans, r-l);
            }
        }
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Your task is to create 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 <bits/stdc++.h>
#define REP(i,n) for(int (i)=0;(i)<(int)(n);(i)++)
using namespace std;

const int N=2000;
bool ab[100000], ac[100000], bc[100000];

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

int main() {
    string a,b,c;
    cin >> a >> b >> c;
    int A=a.length();
    int B=b.length();
    int C=c.length();

    REP(i,A) REP(j,B) if(!match(a[i], b[j])) ab[i-j+50000]=true;
    REP(i,A) REP(j,C) if(!match(a[i], c[j])) ac[i-j+50000]=true;
    REP(i,B) REP(j,C) if(!match(b[i], c[j])) bc[i-j+50000]=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+50000] && !ac[j+50000] && !bc[j-i+50000]) {
                int l=min({0, i, j});
                int r=max({A, B+i, C+j});
                ans=min(ans, r-l);
            }
        }
    }
    cout << ans << endl;
    return 0;
}
```