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)

#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return [LIST() for _ in range(n)]


INF = float("inf")
MOD = 10**9 + 7


def main():
    n, m, q = MAP()
    abcd = ZIP(q)

    def ascending(X):
        for i in range(1, n):
            if A[i - 1] > A[i]:
                return False
        return True

    def point(A):
        tot = 0
        for a, b, c, d in abcd:
            if A[b - 1] - A[a - 1] == c:
                tot += d
        return tot

    def forward(A):
        # Mより小さい最後の桁
        k = None
        for i in reversed(range(n)):
            if A[i] < m:
                k = i
                break
        if k is not None:
            A[k] += 1
            for j in range(k + 1, n):
                A[j] = A[k]
        else:
            A[0] = INF

    # 昇順列を巡回する
    A = [1] * n
    ans = 0
    while ascending(A):         # O(N)
        # print(A)
        p = point(A)
        if ans <= p:
            ans = p
        forward(A)
    print(ans)

    return


if __name__ == '__main__':
    main()