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.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        private int N;
        private int M;
        private int Q;
        private List<QueryItem> queries = new List<QueryItem>();

        private IEnumerable<IReadOnlyList<int>> CreateSequences(IReadOnlyList<int> currentSequence)
        {
            if (currentSequence.Count() == this.N)
            {
                yield return currentSequence;
            }
            else
            {
                var start = currentSequence.Count() > 0 ? currentSequence.Last() : 1;
                foreach (var num in Enumerable.Range(start, this.M - start + 1))
                {
                    var next = new List<int>(currentSequence);
                    next.Add(num);
                    foreach (var sequence in this.CreateSequences(next))
                    {
                        yield return sequence;
                    }
                }
            }
        }

        public void Solve()
        {
            // 入力
            var items = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToArray();
            this.N = items[0];
            this.M = items[1];
            this.Q = items[2];
            foreach (var i in Enumerable.Range(0, Q))
            {
                var items2 = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToArray();
                var a = items2[0];
                var b = items2[1];
                var c = items2[2];
                var d = items2[3];
                this.queries.Add(new QueryItem { a = a, b = b, c = c, d = d });
            }

            // 計算
            var answer = 0L;
            foreach (var sequence in this.CreateSequences(new List<int>()))
            {
                var score = 0;
                foreach (var query in queries)
                {
                    if (sequence[query.b - 1] - sequence[query.a - 1] == query.c)
                    {
                        score += query.d;
                    }
                }

                answer = Math.Max(answer, score);
            }

            Console.WriteLine(answer.ToString());
        }

        public class QueryItem
        {
            public int a { get; set; }
            public int b { get; set; }
            public int c { get; set; }
            public int d { get; set; }
        }
    }
}