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: Accepted)

from pprint import pprint
 
n,m,q = map(int, input().split())
 
ql = [list(map(int,input().split())) for _ in range(q)]
 
#print(n)
#print(m)
#print(q)
#pprint(ls)
 
masterlist = []
minilist = [0] * n
i = 0
 
 
def saiki(before_a,i,minilist):
    if i > n-1:
        masterlist.append([minilist[j] for j in range(n)])
        return
    for Ai in range(before_a,m+1):
        minilist[i] = Ai
        saiki(Ai,i+1,minilist)
 
#for before_a in range(1,m+1):
#    saiki(before_a,where,minilist)
 
before_a = 1
saiki(before_a,i,minilist)
 
#pprint(masterlist)
#pprint(ql)
 
dmax = 0
 
for a_mini in masterlist:
    dtemp = 0
    for ql_mini in ql:
        if a_mini[ql_mini[1]-1] - a_mini[ql_mini[0]-1] == ql_mini[2]:
            dtemp += ql_mini[3]
        else:
            pass
    if dtemp >= dmax:
        dmax = dtemp
 
print(dmax)