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)

def main():
    import copy
    n,m,q=map(int,input().split())
    a=[]
    b=[]
    c=[]
    d=[]
    ans=0
    for i in range(q):
        ai,bi,ci,di=map(int,input().split())
        a.append(ai)
        b.append(bi)
        c.append(ci)
        d.append(di)
    indices = [*range(q)]
    sorted_indices = sorted(indices, key=lambda i: -d[i])
    sorted_num = [d[i] for i in sorted_indices]
    A=[1]*(n+1)
    for i in range(q):
        A[b[i]-1]=c[i]+A[a[i]-1]
    times=0
    for i in sorted_indices:
        #A[b[i]]-A[a[i]]=c[i]→A[b[i]=c[i]+A[a[i]]
        pre=copy.copy(A)
        A[b[i]-1]=c[i]+A[a[i]-1]
        if A[b[i]]>m:
            break
        
        #All Check
        times+=1
        for j in range(1,n+1):
            if A[j]<A[j-1]:
                for k in range(times):
                    si=sorted_indices[k]
                    A[b[si]-1]=c[si]+A[a[si]-1]
        tmp=0
        for j in range(q):
            if A[b[j]-1]-A[a[j]-1]==c[j]:
                tmp+=d[j]
        
        if ans>tmp:
            A=copy.copy(pre)
        ans=max(ans,tmp)
        
    print(ans)
    
    

if __name__=='__main__':
    main()