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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace AtCoder
{
	public class ABC
	{
		static public void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
			Solve(args);
			Console.Out.Flush();
		}

		private const int mod = 1000000007;  // 10^9+7

		static public void Solve(string[] args)
		{
			//string s = Console.ReadLine();
			//int x = int.Parse(Console.ReadLine());
			//long x = long.Parse(Console.ReadLine());
			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] vs = Console.ReadLine().Split().Select(long.Parse).ToArray();
			int n = vs[0];
			int m = vs[1];
			int q = vs[2];

			int[][] list = new int[q][];
			for (int i = 0; i < q; i++) {
				list[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
			}
			int ans = saiki(m, new int[n], 0, list);
			Console.WriteLine(ans);
		}

		static int saiki(int m, int[] A, int i, int[][] Q)
		{
			int ans = 0;
			if (A.Length == i) {
				foreach (var q in Q) {
					int a = q[0] - 1;
					int b = q[1] - 1;
					int c = q[2];
					int d = q[3];
					if (A[b] - A[a] == c) {
						ans += d;
					}
				}
				System.Diagnostics.Debug.WriteLine($"{string.Join(' ', A)} : {ans}");
			} else {
				for (int j = (i == 0 ? 1 : A[i - 1]); j <= m; j++) {
					A[i] = j;
					ans = Math.Max(ans, saiki(m, A, i + 1, Q));
				}
			}
			return ans;
		}

	}
}