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 numpy as np
import math
n, m, q = map(int,input().split())
max = 0
j = []
for i in range(q):
    aa,b,c,d = map(int,input().split())
    j.append([aa,b,c,d])

a = [0 for k in range(11)]
for i1 in range(1,11):
    a[1] = i1
    for i2 in range(i1,11):
        a[2] = i2
        for i3 in range(i2,11):
            a[3] = i3
            for i4 in range(i3,11):
                a[4] = i4
                for i5 in range(i4,11):
                    a[5] = i5
                    for i6 in range(i5,11):
                        a[6] = i6
                        for i7 in range(i6,11):
                            a[7] = i7
                                for i8 in range(i7,11):
                                a[8] = i8
                                    for i9 in range(i8,11):
                                    a[9] = i9
                                        for i10 in range(i9,11):
                                        a[10] = i10
                                        s = 0
                                        for i in j:
                                            if a[i[1]]-a[i[0]] = i[2]:
                                                s += i[3]
                                        if max < s:
                                            max = s

print(max)