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: Wrong Answer)

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

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var nmq = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var (n, m, q) = (nmq[0], nmq[1], nmq[2]);
        var quadraples = new (int a, int b, int c, int d)[q];
        for (int i = 0; i < quadraples.Length; ++i)
        {
            var abcd = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            quadraples[i] = (abcd[0], abcd[1], abcd[2], abcd[3]);
        }

        Array.Sort(quadraples);

        var seqA = new int[n + 2];
        seqA[^1] = m;
        var max = Dfs(seqA, quadraples, 0);

        Console.WriteLine(max);
    }

    static long Dfs(int[] seqA, (int a, int b, int c, int d)[] qs, int index)
    {
        if (index >= qs.Length)
        {
            return qs.Where(x => seqA[x.b] - seqA[x.a] == x.c).Sum(x => x.d);
        }

        var (a, b, c, d) = qs[index++];
        var r = Dfs(seqA, qs, index);

        var bMax = SearchMax(seqA.AsSpan()[(b + 1)..]);
        var aMax = SearchMax(seqA.AsSpan()[(a + 1)..b]);
        if (aMax < 1)
        {
            aMax = bMax - c;
        }

        int k = 1;
        var (aa, ab) = (seqA[a], seqA[b]);
        if (aa < 1 && ab < 1)
        {
            (seqA[a], seqA[b]) = (1, 1 + c);
            k = Math.Min(aMax - seqA[a], bMax - seqA[b]) + 1;
        }
        else if (aa < 1 && 0 < ab - c && ab - c <= aMax)
        {
            seqA[a] = ab - c;
        }
        else if (ab < 1 && aa + c <= bMax)
        {
            seqA[b] = aa + c;
        }
        else if (ab - aa == c)
        {
            // Nothing to do
        }
        else
        {
            k = 0;
        }
        for (int i = 0; i < k; ++i)
        {
            r = Math.Max(r, Dfs(seqA, qs, index));
            ++seqA[a];
            ++seqA[b];
        }
        (seqA[a], seqA[b]) = (aa, ab);

        return r;
    }

    private static int SearchMax(Span<int> xs)
    {
        foreach (var x in xs)
        {
            if (x > 0)
            {
                return x;
            }
        }
        return 0;
    }
}