#include <bits/stdc++.h>

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

using namespace std;
typedef long long ll;
typedef pair<int, int> pint;

constexpr int INF = 1 << 30;
constexpr ll LINF = 1LL << 60;
constexpr int MOD = 1e9 + 7;

constexpr int M = 2000;
bool ab[100000], ac[100000], bc[100000];

bool match(char a, char b) {
    if (a == '?' || b == '?' || a == b) {
        return true;
    } else {
        return false;
    }
}

int main() {
    string a, b, c; cin >> a >> b >> c;
    memset(ab, 1, sizeof(ab));
    memset(ac, 1, sizeof(ac));
    memset(bc, 1, sizeof(bc));
    int A = a.size();
    int B = b.size();
    int C = c.size();

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

    int ans = INF;
    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(i+B, j+C));
                ans = min(ans, r-l);
            }
        }
    }

    cout << ans << endl;


    return 0;
}
### Prompt

Please formulate 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>

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

using namespace std;
typedef long long ll;
typedef pair<int, int> pint;

constexpr int INF = 1 << 30;
constexpr ll LINF = 1LL << 60;
constexpr int MOD = 1e9 + 7;

constexpr int M = 2000;
bool ab[100000], ac[100000], bc[100000];

bool match(char a, char b) {
    if (a == '?' || b == '?' || a == b) {
        return true;
    } else {
        return false;
    }
}

int main() {
    string a, b, c; cin >> a >> b >> c;
    memset(ab, 1, sizeof(ab));
    memset(ac, 1, sizeof(ac));
    memset(bc, 1, sizeof(bc));
    int A = a.size();
    int B = b.size();
    int C = c.size();

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

    int ans = INF;
    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(i+B, j+C));
                ans = min(ans, r-l);
            }
        }
    }

    cout << ans << endl;


    return 0;
}
```