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

namespace AtcoderSubmit
{
    class Program
    {
        private static Value[] _v;

        static void Main(string[] args)
        {
            var line1 = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var n = line1[0];
            var m = line1[1];
            var q = line1[2];
            var v = new Value[q];
            _v = v;
            for(int i = 0; i < v.Length; i++) {
                v[i] = new Value(Console.ReadLine().Split(' '));
            }
            var A = new int[n];
            EachComb(A, m - 1, n);
            Console.WriteLine(_sumMax);
        }

        private static int _sumMax;

        static void EachComb(int[] array, int a, int b)
        {
            if(b == 0) {
                Do(array);
            }
            else {
                if(a < 0) { return; }
                EachComb(array, a - 1, b);
                array[b - 1] = a;
                EachComb(array, a - 1, b - 1);
            }
        }

        static void Do(int[] A)
        {
            var v = _v;
            var sum = 0;
            var str = "";
            for(int i = 0; i < v.Length; i++) {
                if(A[v[i].B-1] - A[v[i].A-1] == v[i].C) {
                    sum += v[i].D;
                    str += " + " + v[i].D.ToString();
                }
            }
            Console.WriteLine($"{string.Join(' ', A)}    : {sum}, {str}");
            _sumMax = Math.Max(sum, _sumMax);
        }


        struct Value
        {
            public int A;
            public int B;
            public int C;
            public int D;
            public Value(string[] line)
            {
                A = int.Parse(line[0]);
                B = int.Parse(line[1]);
                C = int.Parse(line[2]);
                D = int.Parse(line[3]);
            }
        }
    }
}