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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

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

class Program
{
	static int N,M;
	static int maxPt;
	static int[][] abcd;

	//全探索関数
	static void Depth(int[] arr, int ind, int Ai){
			//最終インデックスの場合
			if(ind == N-1){
					//全探索
					for(int i=Ai; i<=M; i++){
							int[] newArr = new int[N];
							Array.Copy(arr, newArr, N);
							newArr[ind] = i;
							ScoreCheck(newArr);
					}
			}
			//最後ではない場合
			else{
					//全探索
					for(int i=Ai; i<=M; i++){
							int[] newArr = new int[N];
							Array.Copy(arr, newArr, N);
							newArr[ind] = i;
							Depth(newArr, ind+1, i);
					}
			}
	}

	//得点をチェックする関数
	static void ScoreCheck(int[] arr){
			int score = 0;

			foreach(int[] nums in abcd){
					if(arr[nums[1]-1] - arr[nums[0]-1] == nums[2]){
								score += nums[3];
					}
			}

			//Console.WriteLine(score);

			if(score > maxPt){
					maxPt = score;
			}
	}

	//Main
	static void Main(string[] args)
	{
		//読み込む
		string[] line = Console.ReadLine().Split(' ');
		N = int.Parse(line[0]);
		M = int.Parse(line[1]);
		int Q = int.Parse(line[2]);

		abcd = new int[Q][];
		for(int i=0; i<Q; i++){
				abcd[i] = new int[4];
				abcd[i] = Console.ReadLine().Split(' ').Select(j => int.Parse(j)).ToArray();
		}

		//An格納する配列
		int[] An = new int[N];

		//全探索を開始
		for(int i=1; i<=M; i++){
				int[] newArr = new int[N];
				Array.Copy(An, newArr, N);
				newArr[0] = i;
				Depth(newArr, 1, i);
		}

		Console.WriteLine(maxPt);

	}
}