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

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            //ここから
            //string[] str = Console.ReadLine().Split(' ');
            //int n = int.Parse(Console.ReadLine());
            string[] str = Console.ReadLine().Split(' ');

            int n = int.Parse(str[0]);
            int m = int.Parse(str[1]);
            int q = int.Parse(str[2]);

            var a = new int[q,4];

            for(int i = 0; i < q; i++)
            {
                str = Console.ReadLine().Split(' ');
                for(int j = 0; j < 4; j++)
                {
                    a[i, j] = int.Parse(str[j]);
                }
            }

            

            var ans = new int[n];
            for (int i = 0; i < n; i++) ans[i] = 1;

            int max = 0;

            while (ans[0]<=m)
            {
                int temp = 0;
                for(int i = 0; i < q; i++)
                {
                    if (ans[a[i, 1]-1] - ans[a[i, 0]-1] == a[i, 2]) temp += a[i, 3];
                }
               // Console.WriteLine("ans={0},{1},{2}, notoki {3}",ans[0],ans[1],ans[2],temp);

                max = Max(max, temp);

                ans[n - 1]++;
                for(int i = n - 1; i > 0; i--)
                {
                    if (ans[i] > m)
                    {
                        ans[i - 1]++;
                        for(int j=i;j<n;j++)
                        ans[j] = ans[i - 1];
                    }
                }

            }

            Console.WriteLine(max);

            //ここまで
        }

        static int Max(int a, int b)
        {
            if (a > b) return a;
            else return b;
        }


    }

}