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>
using namespace std;

vector<vector<int>> make_array(int min_n, int max_n, int length) {
    vector<vector<int>> ans;
    if (length == 1) {
        for (int i = min_n; i < max_n; i++) {
            ans.push_back({i}); 
        }
    }
    else {
        for (int i = min_n; i < max_n; i++){
            vector<vector<int>> ans_sub = make_array(i, max_n, length-1);
            for (int j = 0; j < ans_sub.size(); j++){
                ans_sub[j].insert(ans_sub[j].begin(), {i});
                ans.push_back(ans_sub[j]);
            }
        }
    }
    return ans;
}


int main(){
    int N, M, Q;
    cin >> N >> M >> Q;
    vector<int> a(Q);
    vector<int> b(Q);
    vector<int> c(Q);
    vector<int> d(Q);
    for (int i = 0; i < Q; i++){
        cin >> a[i] >> b[i] >> c[i] >> d[i];
    }
    
    vector<vector<int>> ans_array = make_array(1, M+1, N);

    int ans_max = 0;
    for (int i = 0; i < ans_array.size(); i++){
        int ans = 0;
        if (ans_array[i][0] != 1) break;
        for (int j = 0; j < Q; j++){
            if (ans_array[i][b[j]-1] - ans_array[i][a[j]-1] == c[j]) {
                ans += d[j];
            }
        }
        ans_max = max(ans, ans_max);
    }
    cout << ans_max << endl;
}