#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
template<class T>void chmin(T &a,T b){if(a>b)a=b;}
bool same(char a,char b){
    return (a=='?'||b=='?'||a==b);
}
bool ab[20010],ac[20010],bc[20010];
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    string a,b,c;
    cin>>a>>b>>c;
    int A=a.size(),B=b.size(),C=c.size(),ans=6000;
    rep(i,A){
        rep(j,B){
            if(!same(a[i],b[j]))ab[i-j+10000]=true;
        }
    }
    rep(i,A){
        rep(j,C){
            if(!same(a[i],c[j]))ac[i-j+10000]=true;
        }
    }
    rep(i,B){
        rep(j,C){
            if(!same(b[i],c[j]))bc[i-j+10000]=true;
        }
    }
    for(int i=-4000;i<=4000;i++){
        for(int j=-4000;j<=4000;j++){
            if(!ab[i+10000]&&!ac[j+10000]&&!bc[j-i+10000]){
                int l=min({0,i,j}),r=max({A,B+i,C+j});
                chmin(ans,r-l);
            }
        }
    }
    cout<<ans<<endl;
	return 0;
}
### Prompt

Generate 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>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
template<class T>void chmin(T &a,T b){if(a>b)a=b;}
bool same(char a,char b){
    return (a=='?'||b=='?'||a==b);
}
bool ab[20010],ac[20010],bc[20010];
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    string a,b,c;
    cin>>a>>b>>c;
    int A=a.size(),B=b.size(),C=c.size(),ans=6000;
    rep(i,A){
        rep(j,B){
            if(!same(a[i],b[j]))ab[i-j+10000]=true;
        }
    }
    rep(i,A){
        rep(j,C){
            if(!same(a[i],c[j]))ac[i-j+10000]=true;
        }
    }
    rep(i,B){
        rep(j,C){
            if(!same(b[i],c[j]))bc[i-j+10000]=true;
        }
    }
    for(int i=-4000;i<=4000;i++){
        for(int j=-4000;j<=4000;j++){
            if(!ab[i+10000]&&!ac[j+10000]&&!bc[j-i+10000]){
                int l=min({0,i,j}),r=max({A,B+i,C+j});
                chmin(ans,r-l);
            }
        }
    }
    cout<<ans<<endl;
	return 0;
}
```