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.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		int Q = int.Parse(str[2]);
		int[,]A = new int[Q,4];
		for(var i=0;i<Q;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i,0] = int.Parse(str2[0]);
			A[i,1] = int.Parse(str2[1]);
			A[i,2] = int.Parse(str2[2]);
			A[i,3] = int.Parse(str2[3]);
		}
		int[]B = new int[N];
		for(var i=0;i<N;i++){
			B[i] = 1;
		}
		int t = N-1;
		int ans = 0;
		while(true){
			int ct = 0;
			for(var i=0;i<Q;i++){
				if(B[A[i,1]-1]-B[A[i,0]-1]==A[i,2]){
					ct += A[i,3];
				}
			}
			ans = Math.Max(ans,ct);
			while(B[t]==M){
              t--;
              if(t<0){
                break;
              }
            }
          	if(t<0){
              break;
            }
          	B[t]++;
			for(var x=t;x<N;x++){
				B[x] = B[t];
			}
			t = N-1;
		}
		Console.WriteLine(ans);
	}
}