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;

class Program {

    public struct Pointset {
        public int a;
        public int b;
        public int c;
        public long d;

        public Pointset (int _a, int _b, int _c, long _d) {
            a = _a;
            b = _b;
            c = _c;
            d = _d;
        }
    }

    static void Main (string[] args) {
        string[] S = Console.ReadLine ().Split (' ');
        int N = int.Parse (S[0]);
        int M = int.Parse (S[1]);
        int Q = int.Parse (S[2]);

        int[] A = new int[M];

        Pointset[] pointsets = new Pointset[Q];

        for (int i = 0; i < Q; i++) {
            string[] S1 = Console.ReadLine ().Split (' ');
            pointsets[i] = new Pointset (int.Parse (S1[0]) - 1, int.Parse (S1[1]) - 1, int.Parse (S1[2]), int.Parse (S1[3]));
        }

        long ans = ForeachCombination (M, N, pointsets);
        if (ans < 0) {
            ans = 0;
        }
        Console.WriteLine (ans);
    }

    static long ForeachCombination (int n, int k, Pointset[] pointsets) {
        int[] indexes = new int[k];
        return RecursiveCombination (indexes, n - 1, k, pointsets);
    }

    static long RecursiveCombination (int[] indexes, int s, int rest, Pointset[] pointsets) {
        if (rest == 0) {
            long total = 0;
            foreach (Pointset p in pointsets) {
                if (indexes[p.b] == indexes[p.a] + p.c) {
                    total += p.d;
                }
            }
            return total;
        } else {
            if (s < 0) return -1;
            long max = -1;
            for (int i = 0; i <= s; i++) {
                indexes[rest - 1] = i;
                max = Math.Max (max, RecursiveCombination (indexes, i, rest - 1, pointsets));
            }
            return max;
        }
    }
}