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;

namespace AtCoder {
    class Program {
        static int[][] abcd;
        static int n, m, q;

        static void Main() {
            int[] nmq = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            n = nmq[0];
            m = nmq[1];
            q = nmq[2];
            abcd = new int[q][];
            for(int i = 0; i < q; i++) {
                abcd[i] = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            }

            Console.WriteLine(Solve(new int[0]));
        }
        static long Solve(int[] array) {
            if(array.Length == n) {
                return Score(array);
            }
            long max = 0;
            int last = array.Length == 0 ? 0 : array[ ^ 1];
            for(int i = last; i < m; i++) {
                long score = Solve(array.Append(i).ToArray());
                max = Math.Max(max, score);
            }
            return max;
        }
        static long Score(int[] array) {
            long score = 0;
            for(int i = 0; i < q; i++) {
                int a = abcd[i][0] - 1, b = abcd[i][1] - 1, c = abcd[i][2], d = abcd[i][3];
                if(array[b] - array[a] == c) score += d;
            }
            return score;
        }
    }
}