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;
class Program
{
    static int n;
    static int m;
    static int q;
    static int max;

    static void DFS(int d, int[] X, int cnt, int[,] L)
    {
        if(cnt==n)
        {//正常終了
            for(int i=0; i<n; i++)
            {
                Console.Write(" " + X[i]);
            }
            Console.WriteLine();
            Cir(X, L);
            return;
        }
        if(d == m + 1)
        {//不正終了
            return;
        }
        //dをとらない
        DFS(d + 1, X, cnt, L);
        //dをとる
        X[cnt] = d;
        //重複許す
        DFS(d, X, cnt + 1, L);
        DFS(d + 1, X, cnt + 1, L);
    }
    static void Cir(int[] X, int[,] L)
    {
        int tmp = 0;
        for (int i=0; i<q; i++)
        {            
            if(X[L[i,1]-1]- X[L[i, 0] - 1]== L[i, 2])
            {
                tmp += L[i, 3];
            }
        }
        
        if (tmp > max) max = tmp;
    }
    static void Main()
    {
        string[] In1 = Console.ReadLine().Split(' ');
        n = int.Parse(In1[0]);
        m = int.Parse(In1[1]);
        q = int.Parse(In1[2]);
        string[] In2;
        int[,] L = new int[q, 4];
        for (int i=0; i<q; i++)
        {
            In2 = Console.ReadLine().Split(' ');
            for(int j=0; j < 4; j++)
            {
                L[i, j] = int.Parse(In2[j]);
            }
        }
        int[] X = new int[n];
        DFS(1, X, 0 ,L);
        Console.WriteLine(max);
    }
}