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)

from sys import stdin
import itertools
N,M,Q=list(map(int, (stdin.readline().strip().split())))
num_list=[]
ans_list=[]
score=[]
def judge(ans_list,num):
    count_list=[0]*N
    if (N*(N-1))//2==len(ans_list):return False
    sa=num[2]
    if len(ans_list)!=0:
        min=[ans_list[0][0],ans_list[0][2]]
        max=[ans_list[0][1],ans_list[0][2]]
    else:
        min=[10,0]
        max=[0,0]
    for a,b,c,d in ans_list:
        count_list[a-1]=1
        count_list[b-1]=1
        sa+=c
        if sa>M+1:return False
        if a==num[0] and b==num[1]:return False
        if a==num[0] and b<num[1] and c>num[2]:return False
        if a==num[0] and b>num[1] and c<num[2]:return False
        if b==num[1] and a<num[0] and c<num[2]:return False
        if b==num[1] and a>num[0] and c>num[2]:return False
        if min[0]>=a:min=[a,c+min[1]]
        if max[0]<=b:max=[b,c+max[1]]
    if min[0]==num[0] and max[0]==num[1]:
        c=count_list[num[0]-1:num[1]-1]
        if c.count(0)==0:
            if min[1]+max[1]!=num[2]:return False
        else:
            if min[1] + max[1] > num[2]: return False


    return True
def tansaku(ans_list,num_list,i):


    if i<len(num_list):
        a_list = ans_list.copy()
        b_list = ans_list.copy()
        if judge(ans_list,num_list[i]):
            b_list.append(num_list[i])
            tansaku(b_list,num_list,i+1)
        tansaku(a_list,num_list,i+1)
    else:
        ans=0
        for a,b,c,d  in ans_list:
            ans+=d
        score.append(ans)

for _ in range(Q):
    a,b,c,d=list(map(int, (stdin.readline().strip().split())))
    num_list.append([a,b,c,d])
tansaku(ans_list,num_list,0)
print(max(score))