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 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Scanner;

public class Main { //LeGOD! - Max sequences is 
	//92378 so probably no TLE
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int N = input.nextInt();
		int M = input.nextInt();
		int Q = input.nextInt();
		int[][] query = new int[Q][4];
		for (int i = 0; i < Q; i++) {
			query[i][0] = input.nextInt();
			query[i][1] = input.nextInt();
			query[i][2] = input.nextInt();
			query[i][3] = input.nextInt();
		}
		long ans = 0;
		ArrayList<String> x = Recur(N,M);
		for (int i = 0; i < x.size(); i++) {
			String[] arr = x.get(i).split(" ");
			long curans = 0;
			for (int j = 0; j < Q; j++) {
				int A = query[j][0];
				int B = query[j][1];
				int C = query[j][2];
				int D = query[j][3];
				int cmpA = Integer.parseInt(arr[A-1]);
				int cmpB = Integer.parseInt(arr[B-1]);
				if (cmpB-cmpA==C) curans+=D; 
			}
			ans=Math.max(ans, curans);
		}
		System.out.println(ans);
	}
	public static ArrayList<String> Recur(int N, int M) {
		ArrayList<String> seq = new ArrayList<String>();
		if (N==1) {
			for (int i = 1; i <= M; i++) {
				seq.add(Integer.toString(i)+" "); //Space to prevent confusion of 1 and 10
			}
		}else {
			ArrayList<String> prev = Recur(N-1,M);
			for (int i = 0; i < prev.size(); i++) {
				String[] nums = prev.get(i).split(" ");
				int lowerbound = Integer.parseInt(nums[nums.length-1]);
				for (int j = lowerbound; j <= M; j++) {
					seq.add(prev.get(i)+Integer.toString(j)+" ");
				}
			}
		}
		return seq;
	}
}