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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
        //MyDebugger.Test(process, "../TextFile2.txt");
        //MyDebugger.MakeTestCase("../TextFile2.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var spl = input.ReadLine().Split(' ');
        var n = int.Parse(spl[0]);
        var m = int.Parse(spl[1]);
        var q = int.Parse(spl[2]);

        var AA = new List<int[]>();
        for (int i = 0; i < q; i++) {
            var ary = ToIntArray(input.ReadLine(), 4);
            AA.Add(ary);
        }

        Func<int[], long> count = (A) => {
            long sum = 0;
            foreach(var aa in AA) {
                var ai = aa[0] - 1;
                var bi = aa[1] - 1;
                var ci = aa[2];
                var di = (long)aa[3];
                sum += (A[bi] - A[ai] == ci ? di : 0);
            }
            return sum;
        };


        int[] tmp = new int[n];
        for (int i = 0; i < tmp.Length; i++) tmp[i] = 1;

        long max = 0;
        bool hasNext = true;

        while(hasNext) {
            //print(tmp);
            var sum = count(tmp);
            max = Math.Max(max, sum);

            hasNext = next(tmp, m, 0);
        }

        return max;
    }

    static bool next(int[] A, int max, int p) {
        bool isLast = p == A.Length - 1;
        if (isLast) {
            if (A[p] == max) {
                return false;
            } else {
                A[p] += 1;
                return true;
            }
        }

        var hasNext = next(A, max, p + 1);
        if (hasNext) return true;

        if (A[p] == max) {
            return false;
        } else {
            A[p] += 1;
            A[p + 1] = A[p] - 1;
            next(A, max, p + 1);
            return true;
        }
    }

    static void print(int[] A) {
        var buil = new StringBuilder();
        foreach (var i in A) {
            buil.Append(i);
            buil.Append(',');
        }
        Debug.WriteLine(buil.ToString());
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
}