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

using ll = long long;

bool ab[10000], ac[10000], bc[100000];

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

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    string a, b, c;
    cin >> a >> b >> c;
    for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < b.size(); j++)
            ab[i - j + 5000] |= !match(a[i], b[j]);
    for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < c.size(); j++)
            ac[i - j + 5000] |= !match(a[i], c[j]);
    for (int i = 0; i < b.size(); i++)
        for (int j = 0; j < c.size(); j++)
            bc[i - j + 5000] |= !match(b[i], c[j]);
    int ans = 1 << 30;
    for (int i = -4000; i <= 4000; i++) {
        for (int j = -4000; j <= 4000; j++) {
            if (!ab[i + 5000] && !ac[j + 5000] && !bc[j - i + 5000]) {
                int L = min(0, min(i, j));
                int R = max((int)a.size(),
                            max((int)b.size() + i, (int)c.size() + j));
                ans = min(ans, R - L);
            }
        }
    }
    cout << ans << endl;
}

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

using ll = long long;

bool ab[10000], ac[10000], bc[100000];

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

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    string a, b, c;
    cin >> a >> b >> c;
    for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < b.size(); j++)
            ab[i - j + 5000] |= !match(a[i], b[j]);
    for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < c.size(); j++)
            ac[i - j + 5000] |= !match(a[i], c[j]);
    for (int i = 0; i < b.size(); i++)
        for (int j = 0; j < c.size(); j++)
            bc[i - j + 5000] |= !match(b[i], c[j]);
    int ans = 1 << 30;
    for (int i = -4000; i <= 4000; i++) {
        for (int j = -4000; j <= 4000; j++) {
            if (!ab[i + 5000] && !ac[j + 5000] && !bc[j - i + 5000]) {
                int L = min(0, min(i, j));
                int R = max((int)a.size(),
                            max((int)b.size() + i, (int)c.size() + j));
                ans = min(ans, R - L);
            }
        }
    }
    cout << ans << endl;
}

```