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: Wrong Answer)

import java.util.*;


public class Main {

    private static int Q;
    private static int N;
    private static int M;
    private static int[] a;
    private static int[] b;
    private static int[] c;
    private static int[] d;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        Q = sc.nextInt();
        a = new int[Q];
        b = new int[Q];
        c = new int[Q];
        d = new int[Q];
        int sum = 0;
        for (int i = 0; i < Q; i++) {
            a[i] = sc.nextInt()-1;
            b[i] = sc.nextInt()-1;
            c[i] = sc.nextInt();
            d[i] = sc.nextInt();
            sum += d[i];
        }

        if (Q <= 2) {
            System.out.println(sum);
            return;
        }

        int ans = 0;
        for (int i = 0; i < Q; i++) {
            int[] A = new int[N];
            int ai = a[i];
            int bi = b[i];
            int ci = c[i];

            A[ai] = 1;
            A[bi] = ci+1;
            if (A[bi] > M) continue;
            int tmp = dfs(0, A, ai, bi);
            ans = Math.max(ans,tmp);
        }
        System.out.println(ans);
    }

    private static int dfs(int pos, int[] A, int skip1, int skip2) {
        if (pos == N) {
            return calc(A);
        }
        if (pos == skip1 || pos == skip2) {
            return dfs(pos+1, A, skip1, skip2);
        }


        int max = 0;
        for (int i = 1; i <= M; i++) {
            A[pos] = i;
            int tmp = dfs(pos+1, A, skip1, skip2);
            max = Math.max(max,tmp);
        }

        return max;
    }

    private static int calc(int[] A) {
        int ret = 0;
        for (int i = 0; i < Q; i++) {
            if (A[b[i]]-A[a[i]] == c[i]) ret += d[i];
        }
        return ret;
    }

}