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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>

int N, M, Q;
int seq[50][4];

int calculateScore(std::vector<int> permut)
{
    int score = 0;
    for (int i = 0; i < Q; i++)
    {
        int a = seq[i][0];
        int b = seq[i][1];
        int c = seq[i][2];
        int d = seq[i][3];

        if (permut[b - 1] - permut[a - 1] == c)
        {
            score += d;
        }
    }

    return score;
}

int getMaxScore(int missing, std::vector<int> permut)
{
    if (missing == 0)
    {
        return calculateScore(permut);
    }

    int maxScore = 0;
    int start;
    if (permut.empty())
    {
        start = 1;

    }
    else
    {
        start = permut.back();
    }

    for (int i = start; i <= M; i++)
    {
        permut.push_back(i);
        maxScore = std::max(maxScore, getMaxScore(missing - 1, permut));
        permut.pop_back();
    }

    return maxScore;
}

int main()
{
    std::cin >> N >> M >> Q;

    for (int i = 0; i < Q; i++)
    {
        std::cin >> seq[i][0] >> seq[i][1] >> seq[i][2] >> seq[i][3];
    }

    std::cout << getMaxScore(N, {});
}