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: Wrong Answer)

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

namespace c
{
    class Program
    {

        class HistoryLine
        {
            public IReadOnlyList<int> Nums { get; }
            public int Score { get; }

            public HistoryLine(IReadOnlyList<int> nums, int score)
            {
                this.Nums = nums;
                this.Score = score;
            }
            public HistoryLine GetNext(int num, int addScore)
            {
                return new HistoryLine(this.Nums.Concat(new[] { num }).ToArray(), this.Score + addScore);
            }
        }


        static void Main(string[] args)
        {
            var vals = IOUtils.ReadInts();
            var length = vals[0];
            var maxNum = vals[1];
            var pairCount = vals[2];

            var conds = Enumerable.Repeat(0, pairCount)
                                  .Select(_ => IOUtils.ReadInts())
                                  .Select(ns => new { i1 = ns[0] - 1, i2 = ns[1] - 1, diff = ns[2], score = ns[3] })
                                  .ToList();

            var history = new List<HistoryLine[]>();

            for (int i = 0; i < length; i++)
            {
                if (i == 0)
                {
                    history.Add(new[] { new HistoryLine(new int[] { 1 }, 0) });
                    continue;
                }

                var nexts = new List<HistoryLine>();

                foreach (var before in history.Last())
                {
                    var sameValAdded = false;
                    foreach (var item in conds.Where(c => c.i2 == i))
                    {
                        var newNum = before.Nums[item.i1] + item.diff;
                        if (maxNum < newNum) continue;

                        nexts.Add(before.GetNext(newNum, item.score));

                        if (before.Nums.Last() == newNum)
                        {
                            sameValAdded = true;
                        }
                    }

                    //ひとつ前と同じ数字を入れられるパターンがなければ追加しておく
                    if (!sameValAdded)
                    {
                        nexts.Add(before.GetNext(before.Nums.Last(), 0));
                    }
                }

                history.Add(nexts.ToArray());
            }

            var maxScore = history.Last().Max(h => h.Score);
            Console.WriteLine(maxScore);

        }


        private static IEnumerable<int[]> enumerateArray(int i1, int i2, int expect, int length, int max)
        {
            for (int a1 = 1; a1 <= max; a1++)
            {
                var a2 = a1 + expect;
                if (max < a2) break;

                var res = new int[length];
                res[i1] = a1;
                res[i2] = a2;
                yield return res;
            }
        }
    }

    static class IOUtils
    {
        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        public static ulong ReadUlong()
        {
            return ulong.Parse(Console.ReadLine());
        }
        public static int[] ReadInts()
        {
            return Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
        }
        public static long[] ReadLongs()
        {
            return Console.ReadLine().Split(' ').Select(v => long.Parse(v)).ToArray();
        }

        public static void WriteNums(params int[] nums)
        {
            Console.WriteLine(string.Join(" ", nums));
        }
    }
}