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: Runtime Error)

import math
def fact(n):
    ans = 1
    for i in range(2, n+1):
        ans*= i
    return ans
def comb(n, c):
    return fact(n)//(fact(n-c)*c)
n,m,q = map(int, input().split())
lis = [1 for i in range(n)]
ords = []
cost = []
dp = [-1 for i in range(200)]
ans = 0
for i in range(q):
    o = list(map(int, input().split()))
    ords.append(o[:n])
    cost.append(o[-1])
def checker(p, arr, ans):
    if(dp[p] == ans):
        return dp[p]
    for i in range(n-p-1, -1, -1):
        for c in range(1, m+1):
            arr[p] = c
            temp = 0
            ans = checker(p+1, arr, ans)
            for i in range(q):
                if(arr[ords[i][1]-1]-arr[ords[i][0]-1]==ords[i][2]):
                    temp+=cost[i]
            if(temp > ans):
                ans = temp
            dp[p] = ans
    return ans
print(checker(0, lis, 0))