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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split();
            int n = int.Parse(str[0]);
            int m = int.Parse(str[1]);
            int q = int.Parse(str[2]);

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

            if (m == 1)
            {
                int s = 0;
                for (int i = 0; i < q; ++i)
                    if (tb[i, 2] == 0) s += tb[i, 3];
                Console.WriteLine(s);
                return;
            }

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

            int max = 0;
            while (a[0] == 1)
            {
                int s = 0;
                for (int i = 0; i < q; ++i)
                {
                    int aa = tb[i, 0] - 1;
                    int bb = tb[i, 1] - 1;
                    if (a[bb] - a[aa] == tb[i, 2]) s += tb[i, 3];
                }
                if (max < s) max = s;

                for (int i = n - 1; i >= 0; --i)
                {
                    if (a[i] < m)
                    {
                        ++a[i];
                        for (int j = i; j < n; ++j)
                        {
                            a[j] = a[i];
                        }
                        break;
                    }
                }
            }
            Console.WriteLine(max);
        }
    }
}