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>
using namespace std;

// 入力
int N, M, Q;
vector<long long> a, b, c, d;

// 数列 A のスコアを計算
long long score(const vector<int> &A) {
    long long res = 0;
    for (int i = 0; i < Q; ++i) if (A[b[i]] - A[a[i]] == c[i]) res += d[i];
    return res;
}

// 数列 A を全列挙
long long rec(vector<int> &A) {
    // 終端条件
    if (A.size() == N) return score(A);
    
    // 数列 A の前回要素
    int prev_last = (A.empty() ? 1 : A.back());
    long long res = 0;
    for (int add = prev_last; add <= M; ++add) {
        A.push_back(add);

        // 再帰呼出しながら、スコア最大値を更新
        res = max(res, rec(A)); 
        A.pop_back();
    }
    return res;
}

int main() {
    cin >> N >> M >> Q;
    a.resize(Q); b.resize(Q); c.resize(Q); d.resize(Q);
    for (int q = 0; q < Q; ++q) {
        cin >> a[q] >> b[q] >> c[q] >> d[q];
        --a[q], --b[q];
    }
    vector<int> A;
    cout << rec(A) << endl;
}