#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define REP(i,n) for(int i = 0; i<(int)(n); i++)
#define REPS(i,n) for (int i = 1; i<=(int)(n); i++)
#define REPD(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define FORD(i,a,b) for(int i=(a);i>=(b);i--)
#define pb push_back
#define MOD 1000000007
#define MOD2 998244353

vector<bool> ab(100000, true);
vector<bool> bc(100000, true);
vector<bool> ac(100000, true);

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

int main(){
	string a, b, c;
	cin >> a >> b >> c;
	int A = a.length();
	int B = b.length();
	int C = c.length();

	int i, j;

	REP(i,A) REP(j,B) if (!judge(a[i], b[j])) ab.at(i-j+50000) = false;
	REP(i,A) REP(j,C) if (!judge(a[i], c[j])) ac.at(i-j+50000) = false;
	REP(i,B) REP(j,C) if (!judge(b[i], c[j])) bc.at(i-j+50000) = false;

	int ans = 6000;
	FOR(i,-4000,4000){
		FOR(j,-4000,4000){
			if (ab.at(i+50000) && ac.at(j+50000) && bc.at(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

Please provide a Cpp coded solution to the problem described below:

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;
using ll = long long;
#define REP(i,n) for(int i = 0; i<(int)(n); i++)
#define REPS(i,n) for (int i = 1; i<=(int)(n); i++)
#define REPD(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define FORD(i,a,b) for(int i=(a);i>=(b);i--)
#define pb push_back
#define MOD 1000000007
#define MOD2 998244353

vector<bool> ab(100000, true);
vector<bool> bc(100000, true);
vector<bool> ac(100000, true);

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

int main(){
	string a, b, c;
	cin >> a >> b >> c;
	int A = a.length();
	int B = b.length();
	int C = c.length();

	int i, j;

	REP(i,A) REP(j,B) if (!judge(a[i], b[j])) ab.at(i-j+50000) = false;
	REP(i,A) REP(j,C) if (!judge(a[i], c[j])) ac.at(i-j+50000) = false;
	REP(i,B) REP(j,C) if (!judge(b[i], c[j])) bc.at(i-j+50000) = false;

	int ans = 6000;
	FOR(i,-4000,4000){
		FOR(j,-4000,4000){
			if (ab.at(i+50000) && ac.at(j+50000) && bc.at(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;
}
```