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.LinkedList;
import java.util.Scanner;

public class Main {
	static int n;
	static int m;
	static int q;
	static int a[];
	static int b[];
	static int c[];
	static int d[];
	static int ans;
	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];

		for (int i=0; i<q; i++){
			a[i] = sc.nextInt();
			b[i] = sc.nextInt();
			c[i] = sc.nextInt();
			d[i] = sc.nextInt();
		}

		ans = 0;

		LinkedList<Integer> def = new LinkedList<Integer>();
		def.add(1);
		dfs(def);

		System.out.println(ans);
	}

	public static void dfs(LinkedList<Integer> A){
		if (A.size() == n+1){
			int score = 0;

			for (int i=0; i<q; i++){
				if (A.get(b[i]) - A.get(a[i]) == c[i]){
					score += d[i];
				}
			}

			ans= Math.max(score, ans);
			return;
		}

		A.add(A.getLast());
		while (A.getLast() <= m){
			dfs((LinkedList<Integer>)A.clone());
			A.set(A.size()-1, A.getLast()+1);
		}
	}
}