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;
using System.Text;
using System.Threading.Tasks;
using System.IO;

namespace ABC
{
    class ABC165C
    {
        const bool TESTING = false;
        const string FILE = "/tmp/data.txt";

        static int n;
        static int m;
        static int q;
        static int[] aa;
        static int[] ba;
        static int[] ca;
        static int[] da;

        static long result = 0;

        static void Main(string[] args)
        {
            if (TESTING)
            {
                Console.SetIn(new StreamReader(FILE));
            }
            var line = Console.ReadLine();
            var sa = line.Split(' ');
            n = int.Parse(sa[0]);
            m = int.Parse(sa[1]);
            q = int.Parse(sa[2]);

             aa = new int[q];
             ba = new int[q];
             ca = new int[q];
             da = new int[q];

            for (int i = 0; i < q; ++i)
            {
                line = Console.ReadLine();
                sa = line.Split(' ');
                aa[i] = int.Parse(sa[0]) - 1;
                ba[i] = int.Parse(sa[1]) - 1;
                ca[i] = int.Parse(sa[2]);
                da[i] = int.Parse(sa[3]);
            }

            int[] la = new int[n];
            for (int i = 0; i < n; ++i)
            {
                la[i] = 0;
            }

            proc(la, 0);
            Console.WriteLine(result);
#if DEBUG
            Console.WriteLine();
#endif
        }

        private static void proc(int[] la, int depth)
        {
            if (depth == n)
            {
                // check
                long res = 0;
                for (int i = 0; i < q; ++i)
                {
                    if (la[ba[i]] - la[aa[i]] == ca[i])
                    {
                        res += da[i];
                    }
                }
                if (res > result)
                {
                    result = res;
                }

                return;
            }
            while (la[depth] <= m)
            {
                la[depth] += 1;
                proc(la, depth + 1);
            }
            if (depth > 0)
            {
                la[depth] = la[depth - 1];
            }
        }
    }
}