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;
using System.Numerics;
using System.Diagnostics;

static class Program
{
    class Query
    {
        public readonly int a;
        public readonly int b;
        public readonly int c;
        public readonly int d;
        public Query(int[] args)
        {
            a = args[0];
            b = args[1];
            c = args[2];
            d = args[3];
        }
    }

    class Solver
    {
        public readonly int N;
        public readonly int M;
        public readonly int Q;
        public readonly Query[] queries;
        public Solver(int N, int M, int Q, Query[] queries)
        {
            this.N = N;
            this.M = M;
            this.Q = Q;
            this.queries = queries;
        }
        public int Solve(Stack<int> A)
        {
            if (A.Count == N)
            {
                int sum = 0;
                foreach (var q in queries)
                {
                    if (A.ElementAt(N - q.b) - A.ElementAt(N - q.a) == q.c) { sum += q.d; }
                }
                return sum;
            }
            else
            {
                int max = 0;
                for (int i = A.First(); i <= M; ++i)
                {
                    A.Push(i);
                    max = Math.Max(Solve(A), max);
                    A.Pop();
                }
                return max;
            }
        }
    }

    static long Solve(int N, int M, int Q, Query[] queries)
    {
        return 0;
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int Q = V[2];
        var queries = new Query[Q];
        for (int i = 0; i < Q; ++i)
        {
            queries[i] = new Query(Array.ConvertAll(Console.ReadLine().Split(), int.Parse));
        }
        var A = new Stack<int>();
        A.Push(1);
        Console.WriteLine(new Solver(V[0], V[1], Q, queries).Solve(A));
    }
}