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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();
            int M = sc.nextInt();
            int Q = sc.nextInt();
            int[] a = new int[Q];
            int[] b = new int[Q];
            int[] c = new int[Q];
            int[] d = new int[Q];
            for (int i = 0; i < Q; i++) {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
                c[i] = sc.nextInt();
                d[i] = sc.nextInt();
            }
            int[] A = new int[N + 1];
            A[0] = 1;

            int max = dfs(1, N + 1, M, Q, a, b, c, d, A);

            System.out.println(max);
        }
    }

    private static int dfs(int index, int N, int M, int Q, int[] a, int[] b, int[] c, int[] d, int[] A) {
        if (index >= N) {
            return calculateScore(Q, a, b, c, d, A);
        }

        int max = 0;
        for (int j = A[index - 1]; j <= M; j++) {
            A[index] = j;
            max = Math.max(max, dfs(index + 1, N, M, Q, a, b, c, d, A));
        }
        return max;
    }

    private static int calculateScore(int Q, int[] a, int[] b, int[] c, int[] d, int[] A) {
        int sum = 0;
        for (int i = 0; i < Q; i++) {
            if (A[b[i]] - A[a[i]] == c[i]) {
                sum += d[i];
            }
        }
        return sum;
    }
}