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;

namespace contest_Csharp
{
    class Program
    {
        static long power(long a, long b, long modulo)
        {
            long result = 1;
            long buff = a;
            for (long i = 1; i <= b; i *= 2)
            {
                result = result * ((b / i % (2) == 1) ? buff : 1) % modulo;
                buff = (buff * buff) % modulo;
            }
            return result % modulo;
        }
        static void Main(string[] args)
        {
            var vals = Console.ReadLine().Split(' ')
                .Select(x => int.Parse(x)).ToList();
            int N = vals[0];
            int M = vals[1];
            int Q = vals[2];
            var pairs = new List<(int a, int b,int c,int d)>();
            for (int i = 0; i < Q; i++)
            {
                var Qvals = Console.ReadLine().Split(' ')
                .Select(x => int.Parse(x)).ToList();
                pairs.Add((Qvals[0], Qvals[1], Qvals[2], Qvals[3]));
            }
            Func<IEnumerable<int>, int, int,int> dfs = null;

            dfs = (vec, last ,size) =>
            {
                if (size==N)
                {
                    var V = vec.ToList();
                    return pairs.Where(p => V[p.b - 1] - V[p.a-1] == p.c).Sum(p => p.d);
                }
                return Enumerable.Range(last,M-last+1).Max(x => dfs(vec.Concat(new int[]{ x }), x,size+1));
            };
            Console.WriteLine(dfs(new int[] { 1 }, 1, 1));
        }



    }


}