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.util.Scanner;

public class Main {
    
    static int n, m, q, max;

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        n = Integer.parseInt(sc.next());
        m = Integer.parseInt(sc.next());
        q = Integer.parseInt(sc.next());
        int[][] abcd = new int[q][4];
        for(int i = 0; i < q; i++){
            for(int j = 0; j < 4; j++){
                abcd[i][j] = Integer.parseInt(sc.next());
            }
        }
        max = 0;
        dfs(new int[n+1], abcd, 0);
        System.out.println(max);
    }
    
    static void dfs(int[] a, int[][] abcd, int i){
        if(i > n){
            int point = 0;
            for(int j = 0; j < q; j++){
                if(a[abcd[j][1]] - a[abcd[j][0]] == abcd[j][2]){
                    point += abcd[j][3];
                }
            }
            if(point > max) max = point;
            return;
        }
        
        int k = (i == 0) ? 1 : a[i-1];
        for(int j = k; j <= m; j++){
            a[i] = j;
            dfs(a, abcd, i+1);
        }
    }
}