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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n, m, q = map(int, input().split())

l = []

def inc(ary):
  s = ''
  ary[-1] += 1
  for i in range(len(ary)-1, -1, -1):
    v = ary[i]
    if v > (m - (n-1) + i):
      if i == 0:
        return False
      ary[i-1] += 1
      ary[i] = i+1
  return ary

for i in range(q):
  a, b, c, d = map(int, input().split())
  l.append([a-1, b-1, c, d])

a_tmp = [num for num in range(1, n+1)]
# print(n, m, q)
# print(l)
# print(a_tmp)

ans = 0
l_len = len(l)
while True:
  ans_tmp = 0
  for i in range(l_len):
    a, b, c, d = l[i]
    if (a_tmp[b] - a_tmp[a]) == c:
      ans_tmp += d
  if ans_tmp > ans:
    ans = ans_tmp
  
  # a_tmp のインクリメント
  a_tmp = inc(a_tmp)
  if a_tmp == False:
    break
    
print(ans)