#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <tuple>
#include <cmath>
#include <cstring>

#define rep(i, n) for(int i = 0; i < (int)(n); i++)

using namespace std;
typedef long long ll;

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

const int OFS = 50000;
bool ab[100000];
bool ac[100000];
bool bc[100000];

int main() {
    string a, b, c;
    cin >> a >> b >> c;
    rep(i, a.size()) rep(j, b.size()) if(!match(a[i], b[j])) ab[i-j+OFS] = true;
    rep(i, a.size()) rep(j, c.size()) if(!match(a[i], c[j])) ac[i-j+OFS] = true;
    rep(i, b.size()) rep(j, c.size()) if(!match(b[i], c[j])) bc[i-j+OFS] = true;
    int ans = 6000;
    for (int i = -4000; i <= 4000; i ++) {
        for (int j = -4000; j <= 4000; j ++) {
            if (!ab[i+OFS] && !ac[j+OFS] && !bc[j-i+OFS]) {
                int L = min(0, min(i, j));
                int R = max((int)a.size(), max(i + (int)b.size(), j + (int)c.size()));
                ans = min(ans, R - L);
            }
        }
    }
    cout << ans << endl;
    return 0;
}

### Prompt

In Cpp, your task is to solve 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 <algorithm>
#include <utility>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <tuple>
#include <cmath>
#include <cstring>

#define rep(i, n) for(int i = 0; i < (int)(n); i++)

using namespace std;
typedef long long ll;

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

const int OFS = 50000;
bool ab[100000];
bool ac[100000];
bool bc[100000];

int main() {
    string a, b, c;
    cin >> a >> b >> c;
    rep(i, a.size()) rep(j, b.size()) if(!match(a[i], b[j])) ab[i-j+OFS] = true;
    rep(i, a.size()) rep(j, c.size()) if(!match(a[i], c[j])) ac[i-j+OFS] = true;
    rep(i, b.size()) rep(j, c.size()) if(!match(b[i], c[j])) bc[i-j+OFS] = true;
    int ans = 6000;
    for (int i = -4000; i <= 4000; i ++) {
        for (int j = -4000; j <= 4000; j ++) {
            if (!ab[i+OFS] && !ac[j+OFS] && !bc[j-i+OFS]) {
                int L = min(0, min(i, j));
                int R = max((int)a.size(), max(i + (int)b.size(), j + (int)c.size()));
                ans = min(ans, R - L);
            }
        }
    }
    cout << ans << endl;
    return 0;
}

```