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.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    int m = Integer.parseInt(sc.next());
    int q = Integer.parseInt(sc.next());
    List<Rule> rules = new ArrayList<>();
    for (int i = 0; i < q; i++) {
      rules.add(
        new Rule(
          Integer.parseInt(sc.next()),
          Integer.parseInt(sc.next()),
          Integer.parseInt(sc.next()),
          Integer.parseInt(sc.next())
        )
      );
    }
    RuleList ruleList = new RuleList(rules);
    int array[] = new int[n];
    pw.println(dfs(0, 0, m, array, ruleList));
  }

  static long dfs(int index, long max, int m, int[] array, RuleList ruleList) {
    if (index == array.length) {
      if (!meetCondition(array)) {
        return 0;
      }
      return Math.max(max, ruleList.calc(array));
    }
    if (cut(array, index)) {
      return 0;
    }
    for (int i = 1; i <= m; i++) {
      array[index] = i;
      max = Math.max(max, dfs(index + 1, max, m, array, ruleList));
    }
    return max;
  }

  static boolean cut(int[] array, int index) {
    for (int i = 0; i < index - 1; i++) {
      if (array[i] == 0) {
        return false;
      }
      if (array[i] > array[i + 1]) {
        return true;
      }
    }
    return false;
  }

  static boolean meetCondition(int[] array) {
    for (int i = 0; i < array.length - 1; i++) {
      if (array[i] > array[i + 1]) {
        return false;
      }
    }
    return true;
  }

  static class RuleList {

    private List<Rule> rules;

    RuleList(List<Rule> rules) {
      this.rules = rules;
    }

    long calc(int[] array) {
      return rules.stream().mapToInt(rule -> rule.calc(array)).sum();
    }
  }

  static class Rule {

    int a;
    int b;
    int c;
    int d;

    public Rule(int a, int b, int c, int d) {
      this.a = a;
      this.b = b;
      this.c = c;
      this.d = d;
    }

    int calc(int[] array) {
      if (array[b - 1] - array[a - 1] == c) {
        return d;
      }
      return 0;
    }
  }
}