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)

from collections import defaultdict, deque
from itertools import combinations

N, M, Q = map(int, input().split())
ABCD = [tuple(map(int, input().split())) for _ in range(Q)]

D = defaultdict(set)
for a, b, c, d in ABCD:
  D[b-1].add((a-1, c, d))

for j in range(N-1, 0, -1):
  for x, y in combinations(D[j], 2):
    if x[0] == y[0]:
      continue
    if x[0] > y[0]:
      x, y = y, x
    if x[1] > y[1]:
      for a, c, d in D[y[0]]:
        if a == x[0] and c == x[1] - y[1]:
          break
      else:
        D[y[0]].add((x[0], x[1] - y[1], 0))

for j in range(1, N):
  D[j].add((j-1, 0, 0))

que = deque([([1], 0)])
ans = 0
while que:
  L, score = que.popleft()
  if len(L) == N:
    if score > ans:
      ans = score
  else:
    for a, c, d in D[len(L)]:
      l = L[a] + c
      if l <= M:
        que.append((L + [l], score + sum(d for a, c, d in D[len(L)] if l - L[a] == c)))
print(ans)