#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

const int M = 2000;
const int T = 5 * M;

bool match(char x, char y)
{
	return x == '?' || y == '?' || x == y;
}

int main()
{
	string a, b, c;
	cin >> a >> b >> c;

	int la = a.size();
	int lb = b.size();
	int lc = c.size();

	vector<bool> ab(2 * T, true);
	vector<bool> ac(2 * T, true);
	vector<bool> bc(2 * T, true);

	for (int i = 0; i < la; ++i) {
		for (int j = 0; j < lb; ++j) {
			if (!match(a[i], b[j])) {
				ab[T + i - j] = false;
			}
		}
	}
	for (int i = 0; i < la; ++i) {
		for (int j = 0; j < lc; ++j) {
			if (!match(a[i], c[j])) {
				ac[T + i - j] = false;
			}
		}
	}
	for (int i = 0; i < lb; ++i) {
		for (int j = 0; j < lc; ++j) {
			if (!match(b[i], c[j])) {
				bc[T + i - j] = false;
			}
		}
	}

	int ans = 3 * M;

	for (int i = -2 * M; i <= 2 * M; ++i) {
		for (int j = -2 * M; j <= 2 * M; ++j) {
			if (ab[T + i] && ac[T + j] && bc[T + j - i]) {
				int L = min({ 0, i, j });
				int R = max({ la, i + lb, j + lc });
				ans = min(ans, R - L);
			}
		}
	}
	cout << ans << endl;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 <vector>
#include <string>
#include <algorithm>

using namespace std;

const int M = 2000;
const int T = 5 * M;

bool match(char x, char y)
{
	return x == '?' || y == '?' || x == y;
}

int main()
{
	string a, b, c;
	cin >> a >> b >> c;

	int la = a.size();
	int lb = b.size();
	int lc = c.size();

	vector<bool> ab(2 * T, true);
	vector<bool> ac(2 * T, true);
	vector<bool> bc(2 * T, true);

	for (int i = 0; i < la; ++i) {
		for (int j = 0; j < lb; ++j) {
			if (!match(a[i], b[j])) {
				ab[T + i - j] = false;
			}
		}
	}
	for (int i = 0; i < la; ++i) {
		for (int j = 0; j < lc; ++j) {
			if (!match(a[i], c[j])) {
				ac[T + i - j] = false;
			}
		}
	}
	for (int i = 0; i < lb; ++i) {
		for (int j = 0; j < lc; ++j) {
			if (!match(b[i], c[j])) {
				bc[T + i - j] = false;
			}
		}
	}

	int ans = 3 * M;

	for (int i = -2 * M; i <= 2 * M; ++i) {
		for (int j = -2 * M; j <= 2 * M; ++j) {
			if (ab[T + i] && ac[T + j] && bc[T + j - i]) {
				int L = min({ 0, i, j });
				int R = max({ la, i + lb, j + lc });
				ans = min(ans, R - L);
			}
		}
	}
	cout << ans << endl;
}

```