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 PyPy3 (7.3.0) (judge verdict: Accepted)

from sys import stdin
# import sys
import math


def cmd(n, r):
    return math.factorial(n) // (math.factorial(n - r)*math.factorial(r))


def bts(cnt, A):
    if cnt == N:
        # K += 1
        # print(A)
        global ans
        temp = 0
        for i in range(Q):
            if A[b[i]-1]-A[a[i]-1] == c[i]:
                temp += d[i]
        if temp > ans:
            ans = temp
        # print(ans)
        return
    if len(A) == 0:
        x = 1
    else:
        x = A[-1]
    for i in range(x, M+1):
        # print(i)
        A.append(i)
        bts(cnt+1, A)
        for i in range(cnt, len(A)):
            A.pop()


N, M, Q = [int(x) for x in stdin.readline().rstrip().split()]
# N = [int(x) for x in stdin.readline().rstrip().split()]
# N = int(input())
# U = input().split()
# A, B = [str(x) for x in stdin.readline().rstrip().split()]
global a, b, c, d, ans
ans = 0
a = []
b = []
c = []
d = []
for i in range(Q):
    a1, b1, c1, d1 = [int(x) for x in stdin.readline().rstrip().split()]
    a.append(a1)
    b.append(b1)
    c.append(c1)
    d.append(d1)
global A
A = []
global K
K = 0
cnt = 0
# print(A[K][-1])
bts(cnt, A)
# print(A)
print(ans)