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)

import copy

N, M, Q = map(int, input().split())
abcd_list = []

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


A_list =[-1] * N
sum_max = 0

A_list_list =[]

def dfs(curr, count):
    if count >= N:
        sum_ = 0
        
        for q in range(Q):
            ai = abcd_list[q][0]
            bi = abcd_list[q][1]
            ci = abcd_list[q][2]
            di = abcd_list[q][3]

            if A_list[bi - 1] - A_list[ai - 1] == ci:
                sum_ += di
        global sum_max
        if sum_max <= sum_:
            sum_max = sum_

        A_list_list.append(copy.copy(A_list))

        return

    # 次の値を求める
    for i in range(curr, M + 1):
        A_list[count] = i
        dfs(i, count + 1)

dfs(1, 0)
print(sum_max)