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.Linq;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var NMQ = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        var (N, M, Q) = (NMQ[0], NMQ[1], NMQ[2]);

        var abcd = new (int, int, int, int)[Q];

        for (int i = 0; i < Q; i++)
        {
            var p = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            abcd[i] = (p[0] - 1, p[1] - 1, p[2], p[3]);
        }

        var maxScore = 0;

        foreach (var A in GetA(N, M))
        {
            var score = 0;

            foreach (var (a, b, c, d) in abcd)
            {
                if(A[b] - A[a] == c)
                {
                    score += d;
                }
            }

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

        WriteLine(maxScore);
    }

    static IEnumerable<int[]> GetA(int N, int M)
    {
        var A = Enumerable.Repeat(1, N).ToArray();
        
        yield return A;

        while (true)
        {
            var end = true;

            for (int i = N - 1; 0 <= i; i--)
            {
                if(A[i] < M)
                {
                    A[i]++;

                    for (int j = i + 1; j < N; j++)
                    {
                        A[j] = A[i];
                    }

                    end = false;

                    break;
                }
                else
                {
                    continue;
                }
            }

            if(end)
            {
                break;
            }

            yield return A;
        }
    }
}