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: Wrong Answer)

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<Item> list = new List<Item>();
        private int answer;

        private void Calc(List<int> cur)
        {
            if (cur.Count == this.N)
            {
                var tokuten = 0;
                foreach (var check in list)
                {
                    if (cur[check.b - 1] - cur[check.a - 1] == check.c)
                    {
                        tokuten += check.d;
                    }
                }

                this.answer = Math.Max(this.answer, tokuten);
            }
            else
            {
                var min = cur.Count > 0 ? cur.Last() + 1 : 1;
                for (var i = min; i <= this.M; i++)
                {
                    cur.Add(i);
                    Calc(cur);
                    cur.Remove(cur.Last());
                }
            }
        }

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

        public void Solve()
        {
            var items1 = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToArray();
            this.N = items1[0];
            this.M = items1[1];
            this.Q = items1[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.list.Add(new Item { a = a, b = b, c = c, d = d });
            }

            this.Calc(new List<int>());
            Console.WriteLine(this.answer.ToString());
        }
    }
}