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.*;

public class Main {
 
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    final int N = sc.nextInt(), M = sc.nextInt(), Q = sc.nextInt();
    int[][] abcd = new int[Q][4];
    for(int i=0;i<Q;i++){
      for(int j=0;j<4;j++){
        abcd[i][j] = sc.nextInt();
      }
    }
    Queue<Integer[]> queue = new ArrayDeque<>();
    for(int i=1;i<=M;i++){
      Integer[] arr = {i};
      queue.add(arr);
    }
    while(queue.peek().length < N){
      Integer[] arr = queue.poll();
      int tail = arr[arr.length-1];
      for(int i=tail;i<=M;i++){
      	Integer[] arr_temp = new Integer[arr.length+1];
     	for(int j=0;j<arr.length;j++){
          arr_temp[j] = arr[j];
      	}
        arr_temp[arr_temp.length-1] = i;
        queue.add(arr_temp);
      }
    }
    
    int size = queue.size();
    int score = 0;
    for(int i=0;i<size;i++){
      Integer[] arr = queue.poll();
      int sc_temp = 0;
      for(int j=0;j<Q;j++){
        if(arr[abcd[j][1]-1] - arr[abcd[j][0]-1] == abcd[j][2]){
          sc_temp += abcd[j][3];
        }
      }
      score = Math.max(score, sc_temp);
    }
    System.out.println(score);
  }
  
}