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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nmq = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var q = new IntegerPair[nmq[2]];
            for (var i = 0; i < nmq[2]; i++)
            {
                var abcd = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                q[i] = new IntegerPair { A = abcd[0], B = abcd[1], C = abcd[2], D = abcd[3] };
            }

            var max = 0;
            void Dfs(IEnumerable<int> items)
            {
                var list = items.ToList();
                if (items.Count() == nmq[0])
                {
                    var current = 0;
                    current = q.Where(x => list[x.B - 1] - list[x.A - 1] == x.C).Sum(x => x.D);
                    max = Math.Max(max, current);
                    return;
                }

                var last = list.LastOrDefault();
                list.Add(last != 0 ? last : 1);
                while (list.LastOrDefault() <= nmq[1])
                {
                    Dfs(list);
                    list[list.Count() - 1]++;
                }
            }

            Dfs(new int[] { 1 });
            Console.WriteLine(max);
        }

        public struct IntegerPair
        {
            public int A { get; set; }
            public int B { get; set; }
            public int C { get; set; }
            public int D { get; set; }

        }
    }
}