Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

a?c
der
cod

Sample Output 1

7

For example, s could be atcoder.

Sample Input 2

atcoder
atcoder
???????

Sample Output 2

7

a, b, and c may not be distinct.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
// const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

int main() {
  vector< string > S(3);
  cin >> S;
  sort(begin(S), end(S));
  int ret = inf;
  do {
    vector< int > latte;
    for(int i = 0; i <= S[0].size(); i++) {
      bool match = true;
      for(int j = 0; j < S[1].size() && i + j < S[0].size(); j++) {
        match &= S[1][j] == '?' || S[0][i + j] == '?' || S[1][j] == S[0][i + j];
      }
      if(match) latte.emplace_back(i);
    }
    swap(S[1], S[2]);
    vector< int > malta;
    for(int i = 0; i <= S[0].size(); i++) {
      bool match = true;
      for(int j = 0; j < S[1].size() && i + j < S[0].size(); j++) {
        match &= S[1][j] == '?' || S[0][i + j] == '?' || S[1][j] == S[0][i + j];
      }
      if(match) malta.emplace_back(i);
    }
    swap(S[1], S[2]);

    vector< int > beet(S[1].size() + 1), tap;
    for(int i = 0; i <= S[1].size(); i++) {
      bool match = true;
      for(int j = 0; j < S[2].size() && i + j < S[1].size(); j++) {
        match &= S[2][j] == '?' || S[1][i + j] == '?' || S[2][j] == S[1][i + j];
      }
      beet[i] = match;
      if(match) tap.emplace_back(i);
    }


    for(int i : latte) {
      for(int j : malta) {
        if(i > j) continue;
        if(i + S[1].size() <= j) {
          chmin(ret, max({i + S[1].size(), j + S[2].size(), S[0].size()}));
        } else if(beet[j - i]) {
          chmin(ret, max({i + S[1].size(), j + S[2].size(), S[0].size()}));
        }
      }
    }

    for(int i : latte) {
      for(int j : tap) {
        if(S[0].size() <= i + j) {
          chmin(ret, max({i + S[1].size(), i + j + S[2].size(), S[0].size()}));
        }
      }
    }
  } while(next_permutation(begin(S), end(S)));

  cout << ret << endl;
}