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: Wrong Answer)

#include <bits/stdc++.h>
#define ll long long

using namespace std;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL), cout.tie(NULL);

    int ans = 0, res;
    int a, b, c, d;
    int n, m, q;
    cin >> n >> m >> q;
    vector<vector<int>> v(q, vector<int>(4));
    for(int i = 0; i < q; i++) 
        for(int j = 0; j < 4; j++)
            cin >> v[i][j];
    

    vector<int> seq(n + 1, 1);
    while (1)
    {
        // проверка, что a_i <= a_{i+1}
        int bad = 0;
        for(int i = 1; i < n; i++) {
            if(seq[i] > seq[i + 1]) {
                bad = 1;
                break;
            }
        }
        if(bad) continue;

        // считаем результат (score) строки
        res = 0;
        for (int i = 0; i < q; i++)
        {
            a = v[i][0], b = v[i][1], c = v[i][2], d = v[i][3];
            if ((seq[b] - seq[a]) == c)
                res += d;
        }
        int ans = max(ans, res);

        int good = 0;
        for (int i = n; i >= 1; i--)
        {
            if (seq[i] < m)
            {
                seq[i]++;
                good = 1;
                break;
            }
            else
            {
                continue;
            }
        }
        if(good == 0) {
            cout << ans;
            return 0;
        }
    }
}