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 {

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();

        int N = fs.nextInt();
        int M = fs.nextInt();
        int Q = fs.nextInt();

        int[][] queries = new int[Q][4];

        for (int i = 0; i < Q; ++i) {
            for (int j = 0; j < 4; ++j) {
                queries[i][j] = fs.nextInt();
            }
        }



        // generate all increasing sequences of length N where each element is <= M
        int start = 1;
        int length = 0;
        int[] max = new int[1];
        int[] seq = new int[N];
        int[] num = new int[1];
        dfs(seq, start, length, N, M, max, queries, num);


        System.out.println(max[0]);
    }

    private static void dfs(int[] seq, int start, int length, int N, int M, int[] max, int[][] queries, int[] num) {
        if (length == N) {
            num[0]++;
            max[0] = Math.max(max[0], compute(seq, queries));
            return;
        }
        else {
            for (int k = start; k <= M; ++k) {
                seq[length] = k;
                dfs(seq, k, length + 1, N, M, max, queries, num);
            }
        }
    }

    private static int compute(int[] seq, int[][] queries) {
        int sum = 0;
        for (int i = 0; i < queries.length; ++i) {
            if (seq[queries[i][1] - 1] - seq[queries[i][0] - 1] == queries[i][2]) {
                sum += queries[i][3];
            }
        }

        return sum;
    }
}