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: Runtime Error)

N,M,Q=map(int,input().split())
abcd=[]
for i in range(Q):
    abcdabcd=list(map(int,input().split()))
    abcd.append(abcdabcd)
#入れるAはリスト、[]で表現
def cal(A):
    t=0
    for abcdi in abcd:
        a=abcdi[0]
        b=abcdi[1]
        c=abcdi[2]
        d=abcdi[3]
        if A[b-1]-A[a-1]==c:
            t+=d
    return t

maxi=0
for i in range(1,M+1):
    if M==1:
        maxi=max(maxi,cal([i]))
    for j in range(i,M+1):
        if M==2:
            maxi=max(maxi,cal([i,j]))
        for k in range(j,M+1):
            if M==3:
                maxi=max(maxi,cal([i,j,k]))
            for l in range(k,M+1):
                if M==4:
                    maxi=max(maxi,cal([i,j,k,l]))
                for m in range(l,M+1):
                    if M==5:
                        maxi=max(maxi,cal([i,j,k,l,m]))
                    for n in range(m,M+1):
                        if M==6:
                             maxi=max(maxi,cal([i,j,k,l,m,n]))
                        for o in range(n,M+1):
                            if M==7:
                                maxi=max(maxi,cal([i,j,k,l,m,n,o]))
                            for p in range(o,M+1):
                                if M==8:
                                    maxi=max(maxi,cal([i,j,k,l,m,n,o,p]))
                                for q in range(p,M+1):
                                    if M==9:
                                        maxi=max(maxi,cal([ij,k,l,m,n,o,p,q]))
                                    for r in range(q,M+1):
                                        if M==10:
                                            maxi=max(maxi,cal([i,j,k,l,m,n,o,p,q,r]))
                                        

print(maxi)