#include <bits/stdc++.h>
using namespace std;
#define pp pair<int,int>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define ll long long
#define ld long double
#define all(a) (a).begin(),(a).end()
#define mk make_pair
ll mod=998244353;
int inf=1000001000;
ll INF=1e18+5;
ll MOD=1000000007;

bool ab[100000],ac[100000],bc[100000];

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

int main() {
  int M=2000;
  string a,b,c;
  cin >> a >> b >> c;
  int A=a.size(),B=b.size(),C=c.size();
  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*M;
  for(int i=-2*M;i<=2*M;i++) for(int j=-2*M;j<=2*M;j++){
    if (!ab[i+50000] && !ac[j+50000] && !bc[j-i+50000]){
      int L=min(0,min(i,j));
      int R=max(A,max(B+i,C+j));
      ans=min(ans,R-L);
    }
  }
  cout << ans << endl;
}

### Prompt

Create a solution in Cpp for 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 pp pair<int,int>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define ll long long
#define ld long double
#define all(a) (a).begin(),(a).end()
#define mk make_pair
ll mod=998244353;
int inf=1000001000;
ll INF=1e18+5;
ll MOD=1000000007;

bool ab[100000],ac[100000],bc[100000];

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

int main() {
  int M=2000;
  string a,b,c;
  cin >> a >> b >> c;
  int A=a.size(),B=b.size(),C=c.size();
  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*M;
  for(int i=-2*M;i<=2*M;i++) for(int j=-2*M;j<=2*M;j++){
    if (!ab[i+50000] && !ac[j+50000] && !bc[j-i+50000]){
      int L=min(0,min(i,j));
      int R=max(A,max(B+i,C+j));
      ans=min(ans,R-L);
    }
  }
  cout << ans << endl;
}

```