#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<algorithm>
#include<cmath>
using namespace std;
#define INF 0x3f3f3f3f
const int maxn=1e5+10;
#define _rep(i,a,b) for(int i=(a);i<=(b);++i)
bool ab[maxn],ac[maxn],bc[maxn];
bool match(char c1,char c2)
{
    return c1=='?'||c2=='?'||c1==c2;
}

int main()
{
    #ifdef __LOCAL__
        freopen("1.in","r",stdin);
        freopen("1.out","w",stdout);
    #endif
    string a,b,c;
    cin>>a>>b>>c;
    int A=a.length(),B=b.length(),C=c.length();
    _rep(i,0,A-1)
    {
        _rep(j,0,B-1)
            if(!match(a[i],b[j]))
                ab[i-j+4000]=true;
        _rep(j,0,C-1)
            if(!match(a[i],c[j]))
                ac[i-j+4000]=true;
    }
    _rep(i,0,B-1)
        _rep(j,0,C-1)        
            if(!match(b[i],c[j]))
                bc[i-j+4000]=true;
    int M=2000,ans=3*M;
    for(int i=-2*M;i<=2*M;i++)
        for(int j=-2*M;j<=2*M;j++)
        {
            if(!ab[i+4000]&&!ac[j+4000]&&!bc[j-i+4000])
            {
                int L=min(0,min(i,j));
                int R=max(A,max(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<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<algorithm>
#include<cmath>
using namespace std;
#define INF 0x3f3f3f3f
const int maxn=1e5+10;
#define _rep(i,a,b) for(int i=(a);i<=(b);++i)
bool ab[maxn],ac[maxn],bc[maxn];
bool match(char c1,char c2)
{
    return c1=='?'||c2=='?'||c1==c2;
}

int main()
{
    #ifdef __LOCAL__
        freopen("1.in","r",stdin);
        freopen("1.out","w",stdout);
    #endif
    string a,b,c;
    cin>>a>>b>>c;
    int A=a.length(),B=b.length(),C=c.length();
    _rep(i,0,A-1)
    {
        _rep(j,0,B-1)
            if(!match(a[i],b[j]))
                ab[i-j+4000]=true;
        _rep(j,0,C-1)
            if(!match(a[i],c[j]))
                ac[i-j+4000]=true;
    }
    _rep(i,0,B-1)
        _rep(j,0,C-1)        
            if(!match(b[i],c[j]))
                bc[i-j+4000]=true;
    int M=2000,ans=3*M;
    for(int i=-2*M;i<=2*M;i++)
        for(int j=-2*M;j<=2*M;j++)
        {
            if(!ab[i+4000]&&!ac[j+4000]&&!bc[j-i+4000])
            {
                int L=min(0,min(i,j));
                int R=max(A,max(B+i,C+j));
                ans=min(ans,R-L);
            }
        }
    cout<<ans<<endl;
    return 0;
}
```