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.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramC
    {
        struct Info
        {
            public int a;
            public int b;
            public int c;
            public int d;
        }

        static int _depth, _count;
        static Info[] _list;
        static List<int> _result;

        // 深さ優先探索
        static void dfs(List<int> g)
        {
            if (g.Count == _depth)
            {
                // Console.WriteLine(string.Join("", g));
                _result.Add(calc(g));
                return;
            }

            for (var i = g.Last(); i <= _count; i++)
            {
                g.Add(i);
                dfs(g);
                g.RemoveAt(g.Count - 1);
            }
        }

        static int calc(List<int> g)
        {
            var result = 0;
            foreach (var l in _list)
            {
                if (g[l.b] - g[l.a] == l.c)
                {
                    result += l.d;
                }
            }
            return result;
        }

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

            _depth = n;
            _count = m;

            _list = new Info[q];
            for (var i = 0; i < q; i++)
            {
                var inputs1 = Console.ReadLine().Split(" ");
                _list[i].a = int.Parse(inputs1[0]) - 1;
                _list[i].b = int.Parse(inputs1[1]) - 1;
                _list[i].c = int.Parse(inputs1[2]);
                _list[i].d = int.Parse(inputs1[3]);
            }

            _result = new List<int>();
            for (var i = 1; i <= m; i++)
            {
                dfs(new List<int>() { i });
            }

            Console.WriteLine(_result.Count > 0 ? _result.Max() : 0);
        }
    }
}