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: Accepted)


def main():
    N, M, Q = map(int, input().split())  # 入力

    kumi = []
    for _ in range(Q):
        a, b, c, d = map(int, input().split())
        kumi.append([a, b, c, d])

    A = [1]*N

    flg = True

    s = 0
    ans = None

    while flg:
        # print(A)
        t_s = rtn_score(A, kumi)
        if t_s > s:
            s = t_s
            ans = A
        for i in range(N):
            if A[N - 1 - i] < M:
                A[N - 1 - i] += 1
                break
            else:
                if A[N - 1 - i - 1] < M:
                    A[N - 1 - i - 1] += 1
                    for j in range(i+1):
                        A[N - 1 - j] = A[N - 1 - i - 1]
                    break
            if i == N - 1:  # last
                flg = False

    print(s)


def rtn_score(A, kumi):
    tmp_s = 0
    for k in kumi:
        # print(k)
        # print(k[1])
        if A[k[1]-1] - A[k[0]-1] == k[2]:
            tmp_s += k[3]
    return tmp_s


if __name__ == "__main__":
    main()