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.Linq;
using System.Collections.Generic;

namespace ABC165
{
    class B
    {
        static long N;
        static long M;
        static long Q;
        static long[][] abcd;
        static long ans;
        static void Main(string[] args)
        {
            //var X = long.Parse(Console.ReadLine());
            var NMQ = Console.ReadLine().Split().Select(long.Parse).ToArray();
            N = NMQ[0]; M = NMQ[1]; Q = NMQ[2];
            abcd = Enumerable.Repeat(0, (int)Q).Select(_ => Console.ReadLine().Split().Select(long.Parse).ToArray()).ToArray();

            var list = new List<long>();
            DFS(1, list, N);

            Console.WriteLine(ans);
        }

        static void DFS(int min, List<long> list, long len)
        {
            if (len == 0)
            {
                long sum = 0;
                for (int q = 0; q < Q; q++)
                {
                    if (list[(int)abcd[q][1] - 1] - list[(int)abcd[q][0] - 1] == abcd[q][2]) sum += abcd[q][3];
                }
                ans = Math.Max(ans, sum);
                return;
            }

            for (int i = min; i <= 10; i++)
            {
                list.Add(i);
                DFS(i, list, len - 1);
                list.RemoveAt(list.Count - 1);
            }
        }
    }
}