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.ComponentModel.DataAnnotations;
using System.Globalization;
using System.Linq;


namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] header = Console.ReadLine().Split(' ');
            int length = int.Parse(header[0]);
            int max = int.Parse(header[1]);
            int count = int.Parse(header[2]);
            List<int[]> rowList = new List<int[]>();
            for (int i = 0; i < count; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                rowList.Add(new int[4] { int.Parse(input[0]), int.Parse(input[1]), int.Parse(input[2]), int.Parse(input[3]) });
            }

            int[] suretsu = new int[length];
            int sum = 0;
            int maxsum = 0;
            var hani = Enumerable.Range(1, max);
            var kouholist = Combination.Enumerate<int>(hani, length, false);

            foreach (var k in kouholist)
            {

                foreach (var row in rowList)
                {
                    if (k[row[1] -1] - k[row[0] -1] == row[2])
                    {
                        sum = sum + row[3];
                    }
                }

                if (sum > maxsum)
                {
                    maxsum = sum;
                }

                sum = 0;
            }

            Console.WriteLine(maxsum);

        }

        public static class Combination
        {
            public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
            {
                if (k == 1)
                {
                    foreach (var item in items)
                        yield return new T[] { item };
                    yield break;
                }
                foreach (var item in items)
                {
                    var leftside = new T[] { item };

                    // item よりも前のものを除く （順列と組み合わせの違い)
                    // 重複を許さないので、unusedから item そのものも取り除く
                    var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                    foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                    {
                        yield return leftside.Concat(rightside).ToArray();
                    }
                }
            }
        }
    }
}