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.Linq;

    class Program
    {
        static void Main(string[] args)
        {
            /// スペース区切りの整数の入力
            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);
            int q = int.Parse(input[2]);

            int[] a = new int[q];
            int[] b = new int[q];
            int[] c = new int[q];
            int[] d = new int[q];

            for (int i = 0; i < q; i++)
            {
                input = Console.ReadLine().Split(' ');

                a[i] = int.Parse(input[0]) - 1;
                b[i] = int.Parse(input[1]) - 1;
                c[i] = int.Parse(input[2]);
                d[i] = int.Parse(input[3]);
            }

            var nums = Enumerable.Range(1, m).ToArray();
            var combinations = Combination.Enumerate(nums, n, withRepetition: false);

            int z = 0;
            foreach (var elem in combinations)
            {
                int x = 0;
                for (int i = 0; i < q; i++)
                {
                    if (elem[b[i]] - elem[a[i]] == c[i])
                    {
                        x += d[i];
                    }
                }

                if (x > z)
                {
                    z = x;
                }
            }

            Console.WriteLine(z);
        }
    }

    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();
                }
            }
        }
    }