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 <bits/stdc++.h>

#define rng(i, a, b) for (int i = int(a); i < int(b); i++)
#define rep(i, b) rng(i, 0, b)
#define gnr(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define per(i, b) gnr(i, 0, b)

using namespace std;

using ll = long long;
using P = pair<int, int>;

int n, m, q;
vector<int> a, b, c, d;

ll calcSum(vector<int> &A) {
  ll sum = 0;
  rep(i, q) {
    if (A[b[i]] - A[a[i]] == c[i]) {
      sum += d[i];
    }
  }
  return sum;
}

ll dfs(vector<int> &A) {
  if (A.size() == n) {
    return calcSum(A);
  }
  ll res = INT_MIN;
  int last = A.empty() ? 1 : A.back();
  for (int i = last; i <= m; i++) {
    A.push_back(i);
    res = max(res, dfs(A));
    A.pop_back();
  }
  return res;
}

int main() {
  cin >> n >> m >> q;
  a.resize(q), b.resize(q), c.resize(q), d.resize(q);
  rep(i, q) {
    int aa, bb, cc, dd;
    cin >> aa >> bb >> cc >> dd;
    aa--;
    bb--;
    a.at(i) = aa;
    b.at(i) = bb;
    c.at(i) = cc;
    d.at(i) = dd;
  }
  vector<int> A = vector<int>();
  ll res = dfs(A);
  cout << res << endl;
  return 0;
}