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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            Panasonic.E();
        }
        class Panasonic
        {
            public static void A()
            {
                var A = new int[] { 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, 5, 4, 1, 4, 1, 51 };
                var K = Read.Int();
                Console.WriteLine(A[K - 1]);
            }
            public static void B()
            {
                var H = Read.Long();
                var W = Read.Long();
                if (H == 1 || W == 1) { Console.WriteLine(1);return; }
                Console.WriteLine((H * W + 1) / 2);
            }
            public static void C()
            {
                var A = Read.Long();
                var B = Read.Long();
                var C = Read.Long();
                var cba = (C - B - A);
                var large = cba > 0 && (C - B - A) * (C - B - A) - 4 * A * B > 0;
                Console.WriteLine(large ? "Yes" : "No");
            }
            public static void D()
            {
                var N = Read.Int();
                D_Loop("a", N, 0);
                //var N2 = 1 << (N - 1);
                //List<string> strs = new List<string>();
                //for(int i = 0; i < N2; ++i)
                //{
                //    var s = 0;
                //    var str = "a";
                //    for (int j = 0; j < N - 1; ++j)
                //    {
                //        if((i & (1 << j)) > 0)
                //        {
                //            s++;
                //        }
                //        str = str + (char)('a' + s);
                //    }
                //    strs.Add(str);
                //}
                //strs = strs.OrderBy(x => x).ToList();
                //foreach(var s in strs)
                //{
                //    Console.WriteLine(s);
                //}
            }
            static void D_Loop(string str, int N, int max)
            {
                if (str.Length == N)
                {
                    Console.WriteLine(str);
                    return;
                }
                for(int i = 0; i <= max+1; ++i)
                {
                    D_Loop(str + (char)('a' + i), N, Math.Max(max, i));
                }
            }
            public static void E()
            {
                var A = Read.Str();
                var B = Read.Str();
                var C = Read.Str();
                var AB = MergeList(A, B);
                var AC = MergeList(A, C);
                var BC = MergeList(B, C);
                int min = 1000000;
                for(int i = -4000; i <= 4000; ++i)
                {
                    for(int j = -4000; j <= 4000; ++j)
                    {
                        if(AB[i+10000] && AC[j+10000] && BC[j - i + 10000])
                        {
                            min = Math.Min(min, Math.Max(A.Length, Math.Max(B.Length + i, C.Length + j)) - Math.Min(0, Math.Min(i, j)));
                        }
                    }
                }
                Console.WriteLine(min);
            }
            static bool[] MergeList(string a, string b)
            {
                bool[] ok = Enumerable.Range(0, 20000).Select(i => true).ToArray();
                for (int i = 0; i < a.Length; ++i)
                {
                    for (int j = 0; j < b.Length; ++j)
                    {
                        if(a[i] != '?' && b[j] != '?' && a[i] != b[j])
                        {
                            ok[i - j + 10000] = false;
                        }
                    }
                }
                return ok;
            }
            static int MergeLength(string a, string b, string c, List<int> abPoint)
            {
                HashSet<int> points = new HashSet<int>();
                for (int i = 0; i <= c.Length; ++i)
                {
                    bool ok = true;
                    foreach (var ab in abPoint)
                    {
                        points.Add(ab);
                    }
                    for (int j = 0; j < a.Length; ++j)
                    {
                        if (a.Length > i + j)
                        {
                            if (a[i + j] != '?' && b[j] != '?' && a[i + j] != b[j])
                            {
                                ok = false;
                                break;
                            }
                            foreach(var ab in abPoint)
                            {

                            }
                        }
                    }
                    if (ok)
                    {
                        return Math.Max(a.Length, i + b.Length);
                    }
                }
                return a.Length + b.Length;
            }
            static string Merge(string a, string b)
            {
                for(int i = 0; i <= a.Length; ++i)
                {
                    bool ok = true;
                    for(int j = 0; j < b.Length; ++j)
                    {
                        if (a.Length > i + j)
                        {
                            if (a[i + j] != '?' && b[j] != '?' && a[i + j] != b[j])
                            {
                                ok = false;
                                break;
                            }
                        }
                    }
                    if (ok)
                    {
                        char[] str = new char[Math.Max(a.Length, i + b.Length)];
                        for(int j = 0; j < str.Length; ++j)
                        {
                            if (j < i || b.Length <= j - i)
                            {
                                str[j] = a[j];
                            }
                            else if (j >= a.Length)
                            {
                                str[j] = b[j - i];
                            }
                            else
                            {
                                var aa = a[j];
                                var bb = b[j - i];
                                if (aa == '?' && bb == '?')
                                {
                                    str[j] = '?';
                                }
                                else
                                {
                                    str[j] = aa == '?' ? bb : aa;
                                }
                            }
                        }
                        return String.Join("", str);
                    }
                }
                return null;
            }
            static Tuple<int, int> X_Length(string a)
            {
                List<int> counter = new List<int>();
                int count = 0;
                for(int i = 0; i < a.Length; ++i)
                {
                    if (a[i] == '?') { count++; } else { counter.Add(count);count = 0; }
                }
                counter.Add(count);
                counter.Add(0);
                counter = counter.OrderBy(x => -x).ToList();
                return new Tuple<int, int>(counter[0], counter[1]);
            }
            public static void F()
            {
                var Q = Read.Int();
                for (int i = 0; i < Q; ++i)
                {
                    var ABCD = Read.LongN();
                    var A = ABCD[0];
                    var B = ABCD[1];
                    var C = ABCD[2];
                    var D = ABCD[3];
                    var raw = Math.Abs(C - A) + Math.Abs(D - B);
                    long pow3 = 3;
                    for (int f = 1; f <= 30; ++f)
                    {
                        var a = (A - 1) / pow3;
                        var b = (B - 1) / pow3;
                        var c = (C - 1) / pow3;
                        var d = (D - 1) / pow3;
                        if (a == 1 && c == 1 && Math.Abs(b - d) == 2)
                        {
                            var v1 = a - pow3 + c - pow3;
                            var v2 = pow3 * 4 - a - c;
                            raw += Math.Min(v1, v2);
                        }
                        if (b == 1 && d == 1 && Math.Abs(a - c) == 2)
                        {
                            var v1 = b - pow3 + d - pow3;
                            var v2 = pow3 * 4 - b - d;
                            raw += Math.Min(v1, v2);
                        }
                        pow3 *= 3;
                    }
                    Console.WriteLine(raw);
                }
            }
        }

        class Util
        {
            public static readonly long P = 1000000007;

            public static T[,] Gen<T>(int r, int c, T v)
            {
                var matrix = new T[r, c];
                for (int i = 0; i < r; ++i)
                {
                    for (int j = 0; j < c; ++j)
                    {
                        matrix[i, j] = v;
                    }
                }
                return matrix;
            }

            public static long Sum(long[] array)
            {
                return Sum(array, array.Length);
            }
            public static long Sum(long[] array, int n)
            {
                long total = 0;
                for (int i = 0; i < n; ++i)
                {
                    total += array[i];
                }
                return total;
            }
            public static long Count(long[] array, long x)
            {
                return Count(array, x, array.Length);
            }
            public static long Count(long[] array, long x, int n)
            {
                long total = 0;
                for (int i = 0; i < n; ++i)
                {
                    total += (array[i] == x ? 1 : 0);
                }
                return total;
            }
            public static long[] ASum(long[] array)
            {
                var res = new long[array.Length + 1];
                for (int i = 0; i < array.Length; ++i)
                {
                    res[i + 1] = res[i] + array[i];
                }
                return res;
            }

            public static long GCD(long a, long b)
            {
                while (b > 0)
                {
                    var c = a % b;
                    a = b;
                    b = c;
                }
                return a;
            }
            public static bool IsPrime(long x)
            {
                var fact = Factorize(x);
                return fact.Count == 1 && fact.Values.ElementAt(0) == 1;
            }
            public static Dictionary<long, int> Factorize(long x)
            {
                var dict = new Dictionary<long, int>();
                long minp = 2;
                while (x > 1)
                {
                    bool ok = false;
                    for (long p = minp; p * p <= x; ++p)
                    {
                        if (x % p == 0)
                        {
                            if (!dict.ContainsKey(p))
                            {
                                dict.Add(p, 0);
                            }
                            dict[p]++;
                            minp = p;
                            x /= p;
                            ok = true;
                            break;
                        }
                    }
                    if (!ok)
                    {
                        if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
                        dict[x]++;
                        break;
                    }
                }
                return dict;
            }
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }
            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int, int, long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }
            public static Func<int, int, long> CombinLarge(int mMax, long p)
            {
                var inv = Enumerable.Range(0, mMax + 1).Select(x => Util.Inverse(x, Util.P)).ToArray();
                return (n, m) =>
                {
                    long mult = 1;
                    for (int i = 1; i <= m; ++i)
                    {
                        mult = (((mult * (n + 1 - i)) % Util.P) * inv[i]) % Util.P;
                    }
                    return mult;
                };
            }

            /// <summary>
            /// Calc 2^n mod p
            /// </summary>
            public static long Power2(long n, long p)
            {
                return Power(2, n, p);
            }
            public static long Power(long a, long n, long p)
            {
                long res = 1;
                long mult = a;
                for (int i = 0; i < 40; ++i)
                {
                    if ((n & ((long)1 << i)) > 0)
                    {
                        res = (res * mult) % p;
                    }
                    mult = (mult * mult) % p;
                }
                return res;
            }


            /// <summary>
            /// Thanks to yambe2002-san
            /// </summary>
            public class BST<T> where T : IComparable
            {
                public class Node
                {
                    public T V;
                    public Node L, R;
                    public int Count;
                    public Node(T v) { V = v; Count = 1; }
                }
                static Random _rnd = new Random();
                public static int Count(Node t) { return t == null ? 0 : t.Count; }
                static Node Update(Node t) { t.Count = Count(t.L) + Count(t.R) + 1; return t; }
                public static Node Merge(Node l, Node r)
                {
                    if (l == null || r == null) return l == null ? r : l;
                    if ((double)Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
                    { l.R = Merge(l.R, r); return Update(l); }
                    else { r.L = Merge(l, r.L); return Update(r); }
                }
                public static Tuple<Node, Node> Split(Node t, int k)
                {
                    if (t == null) return new Tuple<Node, Node>(null, null);
                    if (k <= Count(t.L))
                    {
                        var s = Split(t.L, k);
                        t.L = s.Item2;
                        return new Tuple<Node, Node>(s.Item1, Update(t));
                    }
                    else
                    {
                        var s = Split(t.R, k - Count(t.L) - 1);
                        t.R = s.Item1;
                        return new Tuple<Node, Node>(Update(t), s.Item2);
                    }
                }
                public static Node Remove(Node t, T v)
                {
                    if (Find(t, v) == null) return t;
                    return RemoveAt(t, LowerBound(t, v));
                }
                public static Node RemoveAt(Node t, int k)
                {
                    var s = Split(t, k);
                    var s2 = Split(s.Item2, 1);
                    return Merge(s.Item1, s2.Item2);
                }
                public static bool Contains(Node t, T v) { return Find(t, v) != null; }
                public static Node Find(Node t, T v)
                {
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp > 0) t = t.L;
                        else if (cmp < 0) t = t.R;
                        else break;
                    }
                    return t;
                }

                public static Node FindByIndex(Node t, int idx)
                {
                    if (t == null) return null;
                    var currentIdx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        if (currentIdx == idx) return t;
                        if (currentIdx > idx)
                        { t = t.L; currentIdx -= (Count(t == null ? null : t.R) + 1); }
                        else { t = t.R; currentIdx += (Count(t == null ? null : t.L) + 1); }
                    }
                    return null;
                }
                public static int UpperBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var ret = Int32.MaxValue;
                    var idx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);

                        if (cmp > 0)
                        {
                            ret = Math.Min(ret, idx);
                            t = t.L;
                            idx -= (Count(t == null ? null : t.R) + 1);
                        }
                        else if (cmp <= 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static int LowerBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var idx = Count(t) - Count(t.R) - 1;
                    var ret = Int32.MaxValue;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp >= 0)
                        {
                            if (cmp == 0) ret = Math.Min(ret, idx);
                            t = t.L;
                            if (t == null) ret = Math.Min(ret, idx);
                            idx -= t == null ? 0 : (Count(t.R) + 1);
                        }
                        else if (cmp < 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                            if (t == null) return idx;
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static Node Insert(Node t, T v)
                {
                    var ub = LowerBound(t, v);
                    return InsertByIdx(t, ub, v);
                }
                static Node InsertByIdx(Node t, int k, T v)
                {
                    var s = Split(t, k);
                    return Merge(Merge(s.Item1, new Node(v)), s.Item2);
                }
                public static IEnumerable<T> Enumerate(Node t)
                {
                    var ret = new List<T>();
                    Enumerate(t, ret);
                    return ret;
                }
                static void Enumerate(Node t, List<T> ret)
                {
                    if (t == null) return;
                    Enumerate(t.L, ret);
                    ret.Add(t.V);
                    Enumerate(t.R, ret);
                }
            }
            public class Set<T> where T : IComparable
            {
                protected BST<T>.Node _root;
                public T this[int idx] { get { return ElementAt(idx); } }
                public int Count() { return BST<T>.Count(_root); }
                public virtual void Insert(T v)
                {
                    if (_root == null) _root = new BST<T>.Node(v);
                    else
                    {
                        if (BST<T>.Find(_root, v) != null) return;
                        _root = BST<T>.Insert(_root, v);
                    }
                }
                public void Clear() { _root = null; }
                public void Remove(T v) { _root = BST<T>.Remove(_root, v); }
                public bool Contains(T v) { return BST<T>.Contains(_root, v); }
                public T ElementAt(int k)
                {
                    var node = BST<T>.FindByIndex(_root, k);
                    if (node == null) throw new IndexOutOfRangeException();
                    return node.V;
                }
                public int Count(T v) { return BST<T>.UpperBound(_root, v) - BST<T>.LowerBound(_root, v); }
                public int LowerBound(T v) { return BST<T>.LowerBound(_root, v); }
                public int UpperBound(T v) { return BST<T>.UpperBound(_root, v); }
                public Tuple<int, int> EqualRange(T v)
                {
                    if (!Contains(v)) return new Tuple<int, int>(-1, -1);
                    return new Tuple<int, int>(BST<T>.LowerBound(_root, v), BST<T>.UpperBound(_root, v) - 1);
                }
                public List<T> ToList() { return new List<T>(BST<T>.Enumerate(_root)); }
            }
            public class MultiSet<T> : Set<T> where T : IComparable { public override void Insert(T v) { if (_root == null) { _root = new BST<T>.Node(v); } else { _root = BST<T>.Insert(_root, v); } } }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
        }
    }
}