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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System.Linq;
using static System.Math;
using System.Collections.Generic;
using System;

public class Hello
{
    public static int[,] a;
    public static int aL;
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        aL = int.Parse(line[2]);
        a = new int[aL, 4];
        for (int i = 0; i < aL; i++)
        {
            line = Console.ReadLine().Trim().Split(' ');
            for (int j = 0; j < 4; j++)
                a[i, j] = int.Parse(line[j]);
        }
        getAns(n, m);
    }
    static int calc(string s)
    {
        var res = 0;
        for (int i = 0; i < aL; i++)
        {
            var wb = s[a[i, 1] - 1];
            var wa = s[a[i, 0] - 1];
            if (wb - wa == a[i, 2]) res += a[i, 3];
        }
        return res;
    }
    static void getAns(int n, int m)
    {
        var ans = 0;
        var q = new Queue<string>();
        for (int i = 0; i < m; i++) q.Enqueue(i.ToString());
        while (q.Count() > 0)
        {
            var w = q.Dequeue();
            if (w.Length == n) ans = Max(ans, calc(w));
            else
            {
                var wr = w[w.Length - 1] - '0';
                for (int i = wr; i < m; i++) q.Enqueue(w + i.ToString());
            }
        }
        Console.WriteLine(ans);
    }
}