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 = [list(map(int, input().split())) for _ in range(Q)]
j = [1] * N
ans = 0
i = N - 1
k = 0

c = 0

for A in l:
    a, b, c, d = A
    if j[b-1] - j[a-1] == c:
        ans += d

while True:
    
    j[-1] += 1
    ans_ = 0
    for A in l:
        a, b, c, d = A
        if j[b-1] - j[a-1] == c:
            ans_ += d
    if ans_ > ans:
        ans = ans_

    if j[-1] == M + 1:
        for i in range(1, N):
            j[-(i+1)] += 1
            for k in range(N-(i+1), N):
                j[k] = j[-(i+1)]
            if j[-(i+1)] != M + 1:
                break
    if j[0] == M:
        break
print(ans)