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)

n, m, q = input().split()
n = int( n )
m = int( m )
q = int( q )
a = []
b = []
c = []
d = []
for i in range( int( q ) ):
    a_i, b_i, c_i, d_i = input().split()
    a.append( int( a_i ) )
    b.append( int( b_i ) )
    c.append( int( c_i ) )
    d.append( int( d_i ) )

array = [ 1 ] * n
array_list = [ array ]

i = 0
while True:
    for k in range( array_list[i][-1], m + 1 ):
        array_list.append( array_list[i][1:] + [ k ] )
        #print( array_list[i][1:] + [ k ] )
    i = i + 1
    if len( array_list ) > 1200:
        break

max_score = 0
for array in array_list:
    score = 0
    for i in range( q ):
        #print( i, a[i], b[i], c[i], array )
        if array[b[i]-1] - array[a[i]-1] == c[i]:
            score = score + d[i]
    if max_score < score:
        max_score = score

print( max_score )