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)

import sys, math, copy
import numpy as np
sys.setrecursionlimit(10**7)

def returnDepth(node):
    return math.floor(math.log2(node + 1))

def isContradicting(matrix):
    coefMatrix = [[0] * n for i in range(len(matrix))]
    coefMatrix2 = [[0] * (n+1) for i in range(len(matrix))]
    #print(coefMatrix)

    for i in range(len(matrix)):
        coefMatrix[i][matrix[i][0]-1] = 1
        coefMatrix[i][matrix[i][1]-1] = -1
        coefMatrix2[i][matrix[i][0]-1] = 1
        coefMatrix2[i][matrix[i][1]-1] = -1
        coefMatrix2[i][n] = -1 * matrix[i][2]
    
    coef = np.array(coefMatrix)
    coef2 = np.array(coefMatrix2)
    
    return np.linalg.matrix_rank(coef) != np.linalg.matrix_rank(coef2)
    
def DFS(node):
    global point

    parentNode = (node - 1) // 2
    depth = returnDepth(node)

    #print("Node:{}".format(node))
    #print("parentNode:{}".format(parentNode))
    #print("intMatrix[{}]:{}".format(depth-1, intMatrix[depth-1]))
    
    if node > 0:
        tree[node] = copy.copy(tree[parentNode])
        pointList[node] = pointList[parentNode]
        #print("tree[{}]:{}".format(node, tree[node]))
        if node % 2 == 0:
            tree[node].append(intMatrix[depth-1])
            pointList[node] = pointList[node] + intMatrix[depth-1][3]

    #print("tree[{}]:{}".format(node, tree[node]))

    #print(tree[node])
    

    if isContradicting(tree[node]):
        #print("contr")
        return
    elif node >= 2**q - 1:
        #print("pointList[{}]:{}".format(node, pointList[node]))
        if point < pointList[node]:
            point = pointList[node]
        #print(tree[node])
        #print("finish")
    else:
        DFS(2*node+1)
        DFS(2*node+2)
    

n, m, q = list(map(int, input().split()))

intMatrix = []
tree = [[]]*(2**(q + 1) - 1)
pointList = [0]*(2**(q + 1) - 1)

point = 0


for i in range(q):
    intMatrix.append(list(map(int, input().split())))

#print(isContradicting([[2, 4, 1, 86568], [1, 4, 0, 90629], [2, 3, 0, 90310], [3, 4, 1, 29211], [1, 2, 0, 94325]]))

#print(2**(q + 1) - 1)

DFS(0)

print(point)