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.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;

namespace debug
{

    class ProgramC
    {
        //決まっている条件はすべての関数内で作用するようにする
        static int[] a = new int[50];
        static int[] b = new int[50];
        static int[] c = new int[50];
        static int[] d = new int[50];
        static List<int> ans = new List<int>();
        static int n;
        static int m;
        static int q;
        static int[] array = new int[10];//考えた配列

        static void Main(string[] args)
        {
            //入力
            string[] z = Console.ReadLine().Split(' ');
            n = int.Parse(z[0]);
            m = int.Parse(z[1]);
            q = int.Parse(z[2]);

            for (int i = 0; i < q; i++)
            {
                string[] y = Console.ReadLine().Split(' ');
                a[i] = int.Parse(y[0]);
                b[i] = int.Parse(y[1]);
                c[i] = int.Parse(y[2]);
                d[i] = int.Parse(y[3]);

            }

            //最初の文字と入れる場所の位置でDFS
            dfs(1, 0);

            Console.WriteLine(ans.Max());



        }

        /*深さ優先検索*/
        static void dfs(int f,int j)
        {
            if (j == n)
            {
                int count = 0;
                for (int i = 0; i < q; i++)
                {
                    if (array[b[i] - 1] - array[a[i] - 1] == c[i])
                        count += d[i];
                }

                ans.Add(count);//数えたものを入れておく
            }
            else
            {
                for (int c = f; c <= m; c++)
                {
                    array[j] = c;//追加する
                    dfs(c,j+ 1);//次の追加するところと始めるところを決める
                }
            }
        }
    }
}