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: Wrong Answer)

using System;

namespace AtCoder
{
    public static class AtCoder
    {
        public static void Main()
        {
            var input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);
            int q = int.Parse(input[2]);

            var a = new int[q];
            var b = new int[q];
            var c = new int[q];
            var d = new int[q];
            for (int cnt = 0; cnt < q; cnt++)
            {
                input = Console.ReadLine().Split(' ');
                a[cnt] = int.Parse(input[0]);
                b[cnt] = int.Parse(input[1]);
                c[cnt] = int.Parse(input[2]);
                d[cnt] = int.Parse(input[3]);
            }

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

            int ans = 0;
            for (int i = n - 1; i >= 0; i--)
            {
                while (true)
                {
                    int check = 0;
                    for (int j = 0; j < q; j++)
                    {
                        if (test[b[j] - 1] - test[a[j] - 1] == c[j])
                        {
                            check += d[j];
                        }
                    }
                    ans = Math.Max(ans, check);

                    if (test[i] >= m) { break; }
                    test[i]++;
                }
            }

            Console.WriteLine(ans);
        }
    }
}