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.*;
import java.util.*;

public class Main {
    static int res = 0;
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        int n = Integer.parseInt(str[0]);
        int m = Integer.parseInt(str[1]);
        int q = Integer.parseInt(str[2]);

        int[][] Q = new int[q][5];
        for(int i=0; i<q; ++i){
            str = br.readLine().split(" ");
            for(int j=1; j<=4; ++j){
                Q[i][j] = Integer.parseInt(str[j-1]);
            }
        }
        dfs(0,new ArrayList<Integer>(n), n,m,q,Q);
        System.out.println(res);
    }
    public static void dfs(int idx, List<Integer> A, int n,int m, int q,int[][] Q){
        if(idx == n){
            if(A.size() < n) return;
            int score = 0;
            for(int i=0; i<q; ++i){
                if(A.get(Q[i][2]-1) - A.get(Q[i][1]-1) == Q[i][3])
                    score += Q[i][4];
            }
            res = Math.max(res, score);
            return;
        }
        int val = 1;
        if(idx-1 >= 0) {
            val = A.get(idx - 1);
        }
        for(int i=val; i<=m; ++i){
            A.add(i);
            dfs(idx+1,A,n,m,q,Q);
            A.remove(A.size()-1);
        }
    }
}