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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
using namespace std;

struct vst
{
	int a;
	int b;
	int c;
	int d;
};

long search(vector<int> A, int Aindex, int start, int end, vector<vst> condition)
{
	if (Aindex < A.size())
	{ //探索を進める
		long maxscore = 0;
		for (int i = start; i <= end; i++)
		{
			A[Aindex] = i;
			long tmpscore = search(A, Aindex + 1, i, end, condition);
			if (tmpscore > maxscore)
				maxscore = tmpscore;
		}
		return maxscore;
	}
	else
	{ //スコアを求める
		long score = 0;
		for (int i = 0; i < condition.size(); i++)
		{
			if (A[condition[i].b - 1] - A[condition[i].a - 1] == (long)condition[i].c)
				score += condition[i].d;
		}
		return score;
	}
}

int main()
{
	int N; //配列Aの長さ
	int M; //配列Aのとりうる最大値
	int Q; //整数の組の数
	cin >> N >> M >> Q;

	//vst* vsts = new vst[Q]; //整数の組
	vector<vst> condition;
	for (int i = 0; i < Q; i++)
	{
		//cin >> vsts[i].a >> vsts[i].b >> vsts[i].c >> vsts[i].d;
		vst tmp;
		cin >> tmp.a >> tmp.b >> tmp.c >> tmp.d;
		condition.emplace_back(tmp);
	}


	//int* A = new int[N];
	vector<int> A(N);
	long maxscore = 0;
	//cout << search(A, 0, 1, M, vsts) << endl;
	cout << search(A, 0, 1, M, condition) << endl;



	return 0;
}