Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in C# (Mono-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        static void Main(string[] args)
        {
            var r1 = ReadSplit();
            var n1 = r1[0].Int();
            var m1 = r1[1].Int();
            var q1 = r1[2].Int();

            var ll = new List<int[]>();
            var perm = new Permutation();
            foreach (var n in perm.Enumerate(Enumerable.Range(1, m1)))
            {
                var l = new int[n1];
                var isError = false;
                for (int i = 0; i < n1; i++)
                {
                    if (i - 1 > 0 &&  n[i] <= n[i - 1])
                    {
                        isError = true;
                        break;
                    }
                    l[i] = n[i];
                }
                if (isError) continue;
                ll.Add(l);
            }
            var ans = 0D;
            var aaa = new List<int[]>();
            for (int i = 0; i < q1; i++)
            {
                var rr = ReadSplit();
                var aa = rr[0].Int();
                var bb = rr[1].Int();
                var cc = rr[2].Int();
                var dd = rr[3].Int();
                var inta = new int[4];
                inta[0] = aa;
                inta[1] = bb;
                inta[2] = cc;
                inta[3] = dd;
                aaa.Add(inta);
            }
            for (int i = 0; i < ll.Count; i++)
            {
                var total = 0;
                for (int j = 0; j < q1; j++)
                {
                    var aa = aaa[j][0];
                    var bb = aaa[j][1];
                    var cc = aaa[j][2];
                    var dd = aaa[j][3];
                    if (ll[i][bb - 1] - ll[i][aa - 1] == cc)
                    {
                        total += dd;
                    }
                }
                if (ans <= total)
                {
                    ans = total;
                }
            }
            WriteRead(ans);
        }

        public class Permutation
        {
            public IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items)
            {
                return _GetPermutations<T>(new List<T>(), items.ToList());
            }

            private IEnumerable<T[]> _GetPermutations<T>(IEnumerable<T> perm, IEnumerable<T> items)
            {
                if (items.Count() == 0)
                {
                    yield return perm.ToArray();
                }
                else
                {
                    foreach (var item in items)
                    {
                        var result = _GetPermutations<T>(perm.Concat(new T[] { item }),
                                                            items.Where(x => x.Equals(item) == false)
                                        );
                        foreach (var xs in result)
                            yield return xs.ToArray();
                    }
                }
            }
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}