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)

n, m, q = map(int, input().split())
abcd = []
A = 0
B = 1
C = 2
D = 3
for i in range(q):
    abcd.append(list(map(int, input().split())))

for i in range(q):
    abcd[i][A] -= 1
    abcd[i][B] -= 1

ans = 0

for i1 in range(1,m+1):
    for i2 in range(i1,m+1):
        for i3 in range(i2,m+1):
            for i4 in range(i3,m+1):
                for i5 in range(i4,m+1):
                    for i6 in range(i5,m+1):
                        for i7 in range(i6,m+1):
                            for i8 in range(i7,m+1):
                                for i9 in range(i8,m+1):
                                    for i10 in range(i9,m+1):
                                        a = [i1, i2, i3, i4, i5, i6, i7, i8, i9, i10]
                                        now = 0
                                        for j in range(q):
                                            if a[abcd[j][B]] - a[abcd[j][A]] == abcd[j][C]:
                                                now += abcd[j][D]
                                        ans = max(ans, now)

print(ans)