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)

#input = raw_input

#from copy import deepcopy

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

score_dict = {}

for i in range(1, n):
    for j in range(i+1, n+1):
        key = (i, j)
        score_dict[key] = []

all_inputs = []
for i in range(q):
    a, b, c, d = map(int, input().split(" "))
    key = (a, b)
    score_dict[key].append([c, d])
    all_inputs.append([a, b, c, d])

a_list = [set([]) for i in range(n+1)]
a_list[1] = {0}

all_keys = [(i, cur) for cur in range(n+1) for i in range(1, cur)]
used = {}
for key in all_keys:
    pairs = score_dict[key]
    if len(pairs) == 0:
        used[key] = False

    i, j = key
    assert 1 <= i < j
    ais = a_list[i]
    ajs = a_list[j]
    #ais = deepcopy(a_list[i])
    #ajs = deepcopy(a_list[j])
    for c, d in pairs:
        for ai in ais:
            aj = ai + c
            a_list[j].add(aj)

        for aj in ajs:
            ai = aj - c
            if ai < 0:
                continue
            a_list[i].add(ai)


#print(a_list)

all_a_kumis = []

def f(last, last_i):
    if last_i == n:
        all_a_kumis.append(last)
        return

    cur_i = last_i+1
    if len(a_list[cur_i]) == 0:
        a_list[cur_i] = a_list[cur_i-1]
    for a in a_list[cur_i]:
        if last[-1] <= a:
            cur = last + [a]
            f(cur, cur_i)
        
f([0], 1)
#print(all_a_kumis)

out = 0
for cur_as in all_a_kumis:
    cur = 0
    for a, b, c, d in all_inputs:
        a -= 1
        b -= 1
        if cur_as[b] - cur_as[a] == c:
            cur += d
    out = max(out, cur)

print(out)



#last_end_ki = -1
#queues = []
#all_keys = [(i, cur) for cur in range(n+1) for i in range(1, cur)]
#
#last_end_ki = -1
#ki_dict = {}
#for cur in range(2, n+1):
#    start_ki = last_end_ki+1
#    end_ki = start_ki+cur-2
#    #cur_keys = all_keys[start_ki:end_ki+1]
#    ki_dict[cur] = [start_ki, end_ki]
#    last_end_ki += (cur-1)