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# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;

class Program
{
    static int N;
    static int M;
    static int Q;
    static int[] A = new int[10];
    static int[] a = new int[50];
    static int[] b = new int[50];
    static int[] c = new int[50];
    static long[] d = new long[50];

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

        for (var i = 0; i < Q; i++)
        {
            var abcd = Console.ReadLine().Split(' ');
            a[i] = int.Parse(abcd[0]) - 1;
            b[i] = int.Parse(abcd[1]) - 1;
            c[i] = int.Parse(abcd[2]);
            d[i] = long.Parse(abcd[3]);
        }

        var pos = 0;
        var min = 1;
        Console.WriteLine(Sub1(min, pos));
    }

    static long Sub1(int min, int pos)
    {
        long score = 0;

        if (pos == N)
        {
            for(var i = 0; i < Q; i++)
            {
                if (A[b[i]] - A[a[i]] == c[i]) score += d[i];
            }

            return score;
        }

        for (var i = min; i <= M; i++)
        {
            A[pos] = i;
            score = Math.Max(Sub1(i, pos + 1), score);
        }

        return score;
    }
}