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 Python (3.8.2) (judge verdict: Wrong Answer)

def Score(A, a, b, c, d):
	s = 0
	for j in range(len(a)):
		if A[b[j]-1]-A[a[j]-1] == c[j]:
			s += d[j]
	return s

def Increase(A, index, M):
	if A[index] == M:
		Increase(A, index-1, M)
		A[index] = A[index-1]
	else:
		A[index] += 1

n, m, q = list(map(int, input().split()))
a = []
b = []
c = []
d = []
for i in range(q):
	ai, bi, ci, di = list(map(int, input().split()))
	a.append(ai)
	b.append(bi)
	c.append(ci)
	d.append(di)

maximumScore = 0

A = [1]*n

while min(A) != m:
	score = Score(A, a, b, c, d)
	maximumScore = max(maximumScore, score)
	Increase(A, n-1, m)

print(maximumScore)