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.Generic;
using System.Linq;
using System.Text;

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

        var a = new List<int>();
        var b = new List<int>();
        var c = new List<int>();
        var d = new List<int>();
        for (int i = 0; i < Q; i++)
        {
            var line = Console.ReadLine().Split(" ");
            a.Add(int.Parse(line[0]));
            b.Add(int.Parse(line[1]));
            c.Add(int.Parse(line[2]));
            d.Add(int.Parse(line[3]));
        }

        var comb = Combination<int>.Generate(Enumerable.Range(1, M).ToList(), N, true);

        var max = 0;
        foreach (var item in comb)
        {
            var sum = 0;
            for (int i = 0; i < Q; i++)
            {
                var num1 = item[b[i] - 1];
                var num2 = item[a[i] - 1];
                if (num1 - num2 == c[i]) sum += d[i];
            }

            max = Math.Max(sum, max);
        }

        Console.WriteLine(max);
    }

    static class Combination<T>
    {
        private static List<T> _input;
        private static List<List<T>> _comb;

        public static List<List<T>> Generate(List<T> input, int r, bool dupulication)
        {
            _input = new List<T>(input);
            _comb = new List<List<T>>();
            CalcCombination(new List<T>(), r, dupulication);
            return _comb;
        }

        private static void CalcCombination(List<T> list, int r, bool dupulication)
        {
            if (list.Count == r)
            {
                _comb.Add(new List<T>(list));
                return;
            }

            var size = _input.Count;
            var index = 0;
            if (dupulication)
            {
                index = list.Any() ? _input.IndexOf(list.Last()) : 0;
            }
            else
            {
                index = list.Any() ? _input.IndexOf(list.Last()) + 1 : 0;
            }
            for (int i = index; i < size; i++)
            {
                list.Add(_input[i]);
                CalcCombination(list, r, dupulication);
                list.Remove(_input[i]);
            }
        }
    }
}