#include<iostream>
#include<string>
using namespace std;
#define M 2000
bool ab[100000],ac[100000],bc[100000];
bool match(char c1,char c2){
  return(c1== '?' ||c2== '?' ||c1==c2);
}
int main(void){
	int i,j;string a,b,c;
	cin>>a>>b>>c;
	int A=a.length();
	int B=b.length();
	int C=c.length();
  
	for(int i=0;i<A;i++)
	{
		for(int j=0;j<B;j++)
		{
			if(!match(a[i],b[j]))
			{
				ab[i-j+40000] =true;
			}
		}
	}
	for(int i=0;i<A;i++)
	{
		for(int j=0;j<C;j++)
		{
			if(!match(a[i],c[j]))
			{
				ac[i-j+40000] =true;
			}
		}
	}
	for(int i=0;i<B;i++)
	{
		for(int j=0;j<C;j++)
		{
			if(!match(b[i],c[j]))
			{
				bc[i-j+40000] =true;
			}
		}
	}
	
	int ans=3*M;
	for(i=-2*M;i<=2*M;i++)
	{
    	for(j=-2*M;j<=2*M;j++)
    	{
    		if(!ab[i+40000] && !ac[j+40000] &&!bc[j-i+40000])
			{
        		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

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<iostream>
#include<string>
using namespace std;
#define M 2000
bool ab[100000],ac[100000],bc[100000];
bool match(char c1,char c2){
  return(c1== '?' ||c2== '?' ||c1==c2);
}
int main(void){
	int i,j;string a,b,c;
	cin>>a>>b>>c;
	int A=a.length();
	int B=b.length();
	int C=c.length();
  
	for(int i=0;i<A;i++)
	{
		for(int j=0;j<B;j++)
		{
			if(!match(a[i],b[j]))
			{
				ab[i-j+40000] =true;
			}
		}
	}
	for(int i=0;i<A;i++)
	{
		for(int j=0;j<C;j++)
		{
			if(!match(a[i],c[j]))
			{
				ac[i-j+40000] =true;
			}
		}
	}
	for(int i=0;i<B;i++)
	{
		for(int j=0;j<C;j++)
		{
			if(!match(b[i],c[j]))
			{
				bc[i-j+40000] =true;
			}
		}
	}
	
	int ans=3*M;
	for(i=-2*M;i<=2*M;i++)
	{
    	for(j=-2*M;j<=2*M;j++)
    	{
    		if(!ab[i+40000] && !ac[j+40000] &&!bc[j-i+40000])
			{
        		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;
}
```