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: Runtime Error)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

from itertools import product

n, m, q = map(int, readline().split())
abcd = [list(map(int, readline().split())) for _ in range(q)]
ans = 0
for bit in product([1, 0], repeat=q):
    cnt = 0
    aaa = []
    aaaa = set()
    for i, (a, b, c, d) in enumerate(abcd):
        if bit[i] == 1:
            aaa.append([a, b, c])
            cnt += d
    if ans < cnt:
        for a, b, c in aaa:
            for aa, bb, cc in aaa:
                if aa == a and b < bb:
                    aaaa.add([b, bb, cc - c])
                elif aa == a and b > bb:
                    aaaa.add([bb, b, c - cc])
                if b == bb and aa > a:
                    aaaa.add([a, aa, cc - c])
                elif b == bb and aa < a:
                    aaaa.add([aa, a, c - cc])
        aaa += list(aaaa)
        flag = True
        for i, (a, b, c, d) in enumerate(abcd):
            if bit[i] == 1:
                for aa, bb, cc in aaa:
                    if (aa <= a < b <= bb and c > cc) or (a <= aa < bb <= b and c < cc):
                        if aa == a and bb == b and c == cc:
                            continue
                        else:
                            flag = False
                            break
                if not flag:
                    cnt = 0
                    break
        if ans < cnt:
            ans = cnt
print(ans)