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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

 			var inputArray = retreiveLongArray();
			var inputCount = 3;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long N = inputArray[0];
			long M = inputArray[1];
			long Q = inputArray[2];


			var infoList = new List<long[]>();

			for (int i = 0; i < Q; i++) {
				var list = retreiveLongArray();
				infoList.Add(list);
			}


			var nums = Enumerable.Repeat(1, (int)N).ToArray(); 
			

			long max = 0;
			max = DFS(infoList,nums, 0,max,M);

			//答えの出力
			var ans = max;
			Console.WriteLine(ans);

		}

		/// <summary>
		/// DFS
		/// </summary>
		/// <param name="infoList"></param>
		/// <param name="array">A=長さNの整数列</param>
		/// <param name="position"></param>
		/// <param name="max"></param>
		/// <param name="M"></param>
		/// <returns></returns>
		private static long DFS(List<long[]> infoList, int[] array, int position, long max, long M) {

			//一番深いところを調べている場合、採点して返す
			if (position == array.Length - 1) {
				var calc = saiten(infoList, array);
				max = max < calc ? calc : max;
				return max;
			}

			//それ以外の場合、自分より一つ深い階層をループで調べる
			for (int i = array[position]; i <= M; i++) {
				var newArray = array.Select(x => x).ToArray();//参照渡しにならないように
				newArray[position + 1] = i;
				var calc = DFS(infoList, newArray, position + 1, max, M);
				max = max < calc ? calc : max;
			}

			return max;
		}


		/// <summary>
		/// 得点を計算
		/// </summary>
		/// <param name="infoList"></param>
		/// <param name="array"></param>
		/// <returns></returns>
		private static long saiten(List<long[]> infoList, int[] array) {

			long tokuten = 0;
			foreach (var list in infoList) {
				if (array[list[1] - 1] - array[list[0] - 1] == list[2]) {
					tokuten += list[3];
				}
			}
			return tokuten;
		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}

		
	}
}