#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
string a[3];
vec A[3][3];
int main(){
    rep(i,3) cin>>a[i];
    rep(i,3)rep(j,3){
        if(i==j) continue;
        rep(k,a[i].size()){
            int z=1;
            rep(l,min(a[j].size(),a[i].size()-k)) if(a[i][l+k]!=a[j][l]&&a[i][l+k]!='?'&&a[j][l]!='?') z=0;
            A[i][j].push_back(z);
        }
    }
    int ans=a[0].size()+a[1].size()+a[2].size();
    vec B={0,1,2};
    do{
        rep(i,a[B[0]].size()+1)rep(j,max(a[B[0]].size()-i,a[B[1]].size())+1){
            if((i>=a[B[0]].size()||A[B[0]][B[1]][i])&&(j>=a[B[1]].size()||A[B[1]][B[2]][j])&&(i+j>a[B[0]].size()||A[B[0]][B[2]][i+j])) ans=min(ans,int(max({a[B[0]].size(),i+a[B[1]].size(),i+j+a[B[2]].size()})));
        }
    }while(next_permutation(all(B)));
    cout<<ans<<"\n";
}
### Prompt

Please formulate 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++)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
string a[3];
vec A[3][3];
int main(){
    rep(i,3) cin>>a[i];
    rep(i,3)rep(j,3){
        if(i==j) continue;
        rep(k,a[i].size()){
            int z=1;
            rep(l,min(a[j].size(),a[i].size()-k)) if(a[i][l+k]!=a[j][l]&&a[i][l+k]!='?'&&a[j][l]!='?') z=0;
            A[i][j].push_back(z);
        }
    }
    int ans=a[0].size()+a[1].size()+a[2].size();
    vec B={0,1,2};
    do{
        rep(i,a[B[0]].size()+1)rep(j,max(a[B[0]].size()-i,a[B[1]].size())+1){
            if((i>=a[B[0]].size()||A[B[0]][B[1]][i])&&(j>=a[B[1]].size()||A[B[1]][B[2]][j])&&(i+j>a[B[0]].size()||A[B[0]][B[2]][i+j])) ans=min(ans,int(max({a[B[0]].size(),i+a[B[1]].size(),i+j+a[B[2]].size()})));
        }
    }while(next_permutation(all(B)));
    cout<<ans<<"\n";
}
```