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-mcs 6.8.0.105) (judge verdict: Wrong Answer)

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

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

        var abcdList = new List<string>();
        for (int i = 0; i < q; i++)
        {
            var abcd = Console.ReadLine().Split(' ');
            int a = int.Parse(abcd[0]);
            int b = int.Parse(abcd[1]);
            int c = int.Parse(abcd[2]);
            int d = int.Parse(abcd[3]);
            abcdList.Add(a.ToString() + ' ' + b.ToString() + ' ' + c.ToString() + ' ' + d.ToString());
        }

        var nums = Enumerable.Range(1, m).ToArray();
        var combinations = Combination.Enumerate(nums, n, withRepetition: true);
        Console.WriteLine(combinations.Count());
        var scoreList = new List<int>();
        foreach (var elem in combinations)
        {
            var score = 0;
            foreach (var hoge in abcdList)
            {
                var abcd = hoge.Split(' ');
                int a = int.Parse(abcd[0]);
                int b = int.Parse(abcd[1]);
                int c = int.Parse(abcd[2]);
                int d = int.Parse(abcd[3]);

                if (elem[b - 1] - elem[a - 1] == c)
                {
                    score += d;
                }
            }
            scoreList.Add(score);
        }
        Console.WriteLine(scoreList.Max());
    }
}

public static class Combination
{
    public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
    {
        if (k == 1)
        {
            foreach (var item in items)
                yield return new T[] { item };
            yield break;
        }
        foreach (var item in items)
        {
            var leftside = new T[] { item };

            // item よりも前のものを除く （順列と組み合わせの違い)
            // 重複を許さないので、unusedから item そのものも取り除く
            var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

            foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
            {
                yield return leftside.Concat(rightside).ToArray();
            }
        }
    }
}