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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace kozaiyApp
{
    public class C
    {
        static void Main()
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]); // 長さNの整数A
            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++)
            {
                string[] inputN = Console.ReadLine().Split(' ');
                a[i] = int.Parse(inputN[0]);
                b[i] = int.Parse(inputN[1]);
                c[i] = int.Parse(inputN[2]);
                d[i] = int.Parse(inputN[3]);
            }

            int ans = 0;

            // 1 ~ Mのリストを作成
            var L = new List<int>();
            for (int i = 1; i <= M; i++)
            {
                L.Add(i);
            }

            var P = Permutations(L, N); // 順列を列挙

            // 数列ぶん確認
            foreach (var pe in P)
            {
                int an = 0;
                // Q組ぶん確認していく
                for (int i = 0; i < Q; i++)
                {
                    // pe[0], pe[1], pe[2] 数列123
                    int bi = b[i] - 1;
                    int ai = a[i] - 1;
                    if (pe[bi] - pe[ai] == c[i])
                    {
                        an += d[i];
                    }
                }

                // 現在のansより高得点だったら代入
                if (an > ans)
                {
                    ans = an;
                }
            }

            Console.WriteLine(ans);
        }

        static List<List<T>> Permutations<T>(List<T> src, int n)
        {
            // nは1以上かつsrcの長さよりも短い必要がある。
            int len = src.Count;
            if (!(0 < n && n <= len))
            {
                throw new ArgumentOutOfRangeException();
            }

            var permutations = new List<List<T>>();
            var queue = new Queue<List<int>>(Enumerable.Range(0, len).Select(i => new List<int>() { i }));
            while (queue.Any())
            {
                var indexes = queue.Dequeue();

                if (indexes.Count == n)
                {
                    permutations.Add(indexes.Select(index => src[index]).ToList());
                    continue;
                }

                for (int index = 0; index < len; index++)
                {
                    if (indexes.Contains(index))
                    {
                        continue;
                    }

                    var newIndexes = new List<int>(indexes);
                    newIndexes.Add(index);
                    queue.Enqueue(newIndexes);
                }
            }

            return permutations;
        }
    }
}