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: Runtime Error)

#region いつもの
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static Global;
using static NumGlobal;

static class Global
{
    public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value);
    public static T[] NewArray<T>(int len0, Func<T> factory)
    {
        var arr = new T[len0];
        for (int i = 0; i < arr.Length; i++) arr[i] = factory();
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value);
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, Func<T> factory)
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory)
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory)
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory);
        return arr;
    }
    private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
    public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
    public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
}
static class NumGlobal
{
    public static long Pow(long x, int y)
    {
        long res = 1;
        for (; y > 0; y >>= 1)
        {
            if ((y & 1) == 1) res *= x;
            x *= x;
        }
        return res;
    }
    public static BigInteger ParseBigInteger(string s)
    {
        // MonoのBigInteger.Parseが遅いので自前実装
        var res = BigInteger.Zero;
        var splited = new string[(s.Length + 7) / 8];
        for (var i = 0; i < splited.Length - 1; i++)
        {
            splited[i] = s.Substring(8 * i, 8);
        }
        splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
        foreach (var sp in splited)
        {
            res *= (int)Math.Pow(10, sp.Length);
            res += int.Parse(sp);
        }
        return res;
    }
    public static int BitCount(int x) { x -= (x >> 1) & 0x55555555; x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x + (x >> 4)) & 0x0f0f0f0f; x += x >> 8; x += x >> 16; return x & 0x3f; }
    public static int BitCount(long x) { x -= (x >> 1) & 0x5555555555555555; x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x += x >> 8; x += x >> 16; x += x >> 32; return (int)(x & 0x0000007f); }
    public static int MSB(int x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return BitCount(x) - 1; }
    public static int MSB(long x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; x |= x >> 32; return BitCount(x) - 1; }
    public static int LSB(int x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; return 32 - BitCount(x); }
    public static int LSB(long x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; x |= x << 32; return 64 - BitCount(x); }
}
static class Ext
{
    public static T[] Fill<T>(this T[] arr, T value)
    {
        for (var i = 0; i < arr.Length; i++) arr[i] = value;
        return arr;
    }
    public static T[] Sort<T>(this T[] arr)
    {
        Array.Sort(arr);
        return arr;
    }
    public static string[] Sort(this string[] arr)
    {
        Array.Sort(arr, StringComparer.OrdinalIgnoreCase);
        return arr;
    }
    public static T[] Reverse<T>(this T[] arr)
    {
        Array.Reverse(arr);
        return arr;
    }

    public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
        (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
        where TMax : IComparable<TMax>
    {
        TMax max;
        TSource maxByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        maxByItem = e.Current;
        max = maxBySelector(maxByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = maxBySelector(item);
            if (max.CompareTo(next) < 0)
            {
                max = next;
                maxByItem = item;
            }
        }
        return Tuple.Create(maxByItem, max);
    }
    public static Tuple<TSource, TMin> MinBy<TSource, TMin>
        (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
        where TMin : IComparable<TMin>
    {
        TMin min;
        TSource minByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        minByItem = e.Current;
        min = minBySelector(minByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = minBySelector(item);
            if (min.CompareTo(next) > 0)
            {
                min = next;
                minByItem = item;
            }
        }
        return Tuple.Create(minByItem, min);
    }
    public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
    public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
    public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
}
#pragma warning disable CA1819
[System.Diagnostics.DebuggerNonUserCode]
public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String { get; } } public SplitLine Split => new SplitLine(this); public class RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (int i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public string[] String => this.Select(cr => cr.String); public int[] Int => this.Select(cr => cr.Int); public int[] Int0 => this.Select(cr => cr.Int - 1); public long[] Long => this.Select(cr => cr.Long); public double[] Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
public class Program
{
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;

    public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
    static void Main(string[] args) => Console.WriteLine(new Program(new ConsoleReader(args.Length > 0 ? new System.IO.StreamReader(args[0]) : Console.In)).Calc());

    #endregion
    public object Calc()
    {
        var N = cr.Int;

        pows[0] = 1;
        for (int i = 1; i < pows.Length; i++)
            pows[i] = pows[i - 1] * 3;

        var res = new long[N];
        for (int i = 0; i < N; i++)
        {
            var a = cr.Long - 1; var b = cr.Long - 1;
            var c = cr.Long - 1; var d = cr.Long - 1;
            res[i] = CalcImpl(a, b, c, d, 29);
        }
        return AllLines(res);
    }

    long[] pows = new long[31];
    long CalcImpl(long a, long b, long c, long d, int size)
    {
        var po = pows[size];//3^29
        while (a / po == c / po && b / po == d / po)
        {
            size--;
            po /= 3;
        }
        while (true)
        {
            var pp = po * 3;
            var ps = po / 3;

            // ブロックが斜めに違うならまっすぐ行ける
            if (a / po != c / po && b / po != d / po)
                return Math.Abs(a - c) + Math.Abs(b - d);

            // 縦横のブロックが同じだと困る
            // とりあえず横のブロックが同じのときは縦が同じになるように入れ替える
            if (a / po == c / po)
            {
                Swap(ref a, ref b);
                Swap(ref c, ref d);
            }

            // aの方が小さくなるようにする
            if (a > c)
            {
                Swap(ref a, ref c);
                Swap(ref b, ref d);
            }

            a %= pp; b %= pp; c %= pp; d %= pp;
            if (size == 0)
            {
                if (b / po == 1)
                    return 4;
                else
                    return c - a;
            }
            if (b / po == 1)
                return Math.Min(b - (po - 1) + d - (po - 1), 2 * po - b + 2 * po - d) + Math.Abs(a - c);

            if (c - 1 == a)
                return Math.Abs(c - a) + Math.Abs(b - d);

            if ((b % po) / ps != (d % po) / ps)
                return Math.Abs(a - c) + Math.Abs(b - d);
            if ((a % po) / ps == 0)
                return 1 + c % po + (c / po - a / po - 1) * po + CalcImpl(a % po, b, po - 1, d, size - 1);
            else if ((c % po) / ps == 2)
                return (po - a % po) + (c / po - a / po - 1) * po + CalcImpl(0, b, c % po, d, size - 1);
            else if (c / po - a / po == 2)
                return (po - a % po) + 1 + c % po + CalcImpl(0, b, 3 * po - 1, d, size - 1);
            else
                return CalcImpl(a % ps, b % ps, c % ps + (c - (a / ps * ps)) / ps * ps, d % ps, size);
        }

    }
    static void Swap<T>(ref T a, ref T b)
    {
        T tmp;
        tmp = a;
        a = b;
        b = tmp;
    }
}