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

const int M = 2005;
const int N = 30005;
const int o = 15000;

bool ab[N],ac[N],bc[N];

bool match(char x,char y) {
    return x=='?' || y=='?' || x==y;
}

string a,b,c;
int la,lb,lc;

signed main() {
    ios::sync_with_stdio(false);
    cin>>a>>b>>c;
    la=a.length();
    lb=b.length();
    lc=c.length();
    for(int i=0;i<la;i++) for(int j=0;j<lb;j++)
        if(ab[i-j+o]==0&&!match(a[i],b[j])) ab[i-j+o]=1;
    for(int i=0;i<la;i++) for(int j=0;j<lc;j++)
        if(ac[i-j+o]==0&&!match(a[i],c[j])) ac[i-j+o]=1;
    for(int i=0;i<lb;i++) for(int j=0;j<lc;j++)
        if(bc[i-j+o]==0&&!match(b[i],c[j])) bc[i-j+o]=1;
    int ans=N;
    for(int i=-2*M;i<=2*M;i++) for(int j=-2*M;j<=2*M;j++) {
        if(!ab[i+o] && !ac[j+o] && !bc[j-i+o]) {
            ans=min(ans, max(la,max(lb+i,lc+j))-min(0,min(i,j)));
        }
    }
    cout<<ans<<endl;
}
### 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;

const int M = 2005;
const int N = 30005;
const int o = 15000;

bool ab[N],ac[N],bc[N];

bool match(char x,char y) {
    return x=='?' || y=='?' || x==y;
}

string a,b,c;
int la,lb,lc;

signed main() {
    ios::sync_with_stdio(false);
    cin>>a>>b>>c;
    la=a.length();
    lb=b.length();
    lc=c.length();
    for(int i=0;i<la;i++) for(int j=0;j<lb;j++)
        if(ab[i-j+o]==0&&!match(a[i],b[j])) ab[i-j+o]=1;
    for(int i=0;i<la;i++) for(int j=0;j<lc;j++)
        if(ac[i-j+o]==0&&!match(a[i],c[j])) ac[i-j+o]=1;
    for(int i=0;i<lb;i++) for(int j=0;j<lc;j++)
        if(bc[i-j+o]==0&&!match(b[i],c[j])) bc[i-j+o]=1;
    int ans=N;
    for(int i=-2*M;i<=2*M;i++) for(int j=-2*M;j<=2*M;j++) {
        if(!ab[i+o] && !ac[j+o] && !bc[j-i+o]) {
            ans=min(ans, max(la,max(lb+i,lc+j))-min(0,min(i,j)));
        }
    }
    cout<<ans<<endl;
}
```