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 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Silviase
 */
public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CManyRequirements solver = new CManyRequirements();
        solver.solve(1, in, out);
        out.close();
    }

    static class CManyRequirements {

        private int n;
        private int m;
        private int q;
        private int[] a;
        private int[] b;
        private int[] c;
        private int[] d;
        private int max = 0;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();
            q = in.nextInt();
            a = new int[q];
            b = new int[q];
            c = new int[q];
            d = new int[q];
            for (int i = 0; i < q; i++) {
                a[i] = in.nextInt() - 1;
                b[i] = in.nextInt() - 1;
                c[i] = in.nextInt();
                d[i] = in.nextInt();
            }

            ArrayList<Integer> al = new ArrayList<>();
            dfs(al);
            out.println(max);
        }

        private void dfs(ArrayList<Integer> list) {
            // System.out.println(list.size() + " " + list);

            if (list.size() >= n) {
                max = Math.max(max, calc(list));
                // System.out.println("ret");
                return;
            }

            for (int i = list.size() == 0 ? 1 : list.get(list.size() - 1); i <= m; i++) {
                list.add(i);
                dfs(list);
                list.remove(list.size() - 1);
            }
        }

        private int calc(ArrayList<Integer> list) {
            int cmp = 0;
            for (int i = 0; i < q; i++) {
                if (list.get(b[i]) - list.get(a[i]) == c[i]) {
                    cmp += d[i];
                }
            }
            return cmp;
        }

    }
}