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 <cstdio>

int n, m, q;
int tuple[50][4];
int array[10];

int dfs(int index, int last)
{
	if (index >= 0)
	{
		array[index] = last;

		if (index == n - 1)
		{
			int r = 0;
			for (int i = 0; i < q; ++i)
			{
				if (array[tuple[i][1] - 1] - array[tuple[i][0] - 1] == tuple[i][2])
				{
					r += tuple[i][3];
				}
			}
			return r;
		}
	}

	int r = 0;
	for (int i = last; i <= m; ++i)
	{
		int v = dfs(index + 1, i);
		if (v > r)
		{
			r = v;
		}
	}
	return r;
}

int main()
{
	scanf("%d%d%d", &n, &m, &q);
	for (int i = 0; i < q; ++i)
	{
		scanf("%d%d%d%d", tuple[i], tuple[i] + 1, tuple[i] + 2, tuple[i] + 3);
	}
	int ans = dfs(-1, 1);
	printf("%d\n", ans);
	return 0;
}