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>
using namespace std;
using lint = int64_t;
namespace my {
char itoc(int i) { return i + '0'; }
int ctoi(char c) { return c - '0'; }
lint gcd(lint a, lint b) {
  a = abs(a);
  b = abs(b);
  if (a < b) swap(a, b);
  while (b != 0) {
    a %= b;
    swap(a, b);
  }
  return a;
}
lint lcm(lint a, lint b) { return a * b / my::gcd(a, b); }
}  // namespace my
/*                    */

void choufukucomb(vector<vector<int>> &zembu, vector<int> tmp, int &n, int &m) {
  if (tmp.size() == n)
    zembu.push_back(tmp);
  else if (tmp.empty()) {
    for (int i = 1; i <= m; i++) {
      tmp.push_back(i);
      choufukucomb(zembu, tmp, n, m);
      tmp.pop_back();
    }
  } else {
    for (int i = *tmp.rbegin(); i <= m; i++) {
      tmp.push_back(i);
      choufukucomb(zembu, tmp, n, m);
      tmp.pop_back();
    }
  }
}

int main() {
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> a, b, c, d;
  for (int i = 0; i < q; i++) {
    int tmp;
    cin >> tmp;
    a.push_back(--tmp);
    cin >> tmp;
    b.push_back(--tmp);
    cin >> tmp;
    c.push_back(tmp);
    cin >> tmp;
    d.push_back(tmp);
  }

  vector<vector<int>> zembu;
  vector<int> kyomu;
  choufukucomb(zembu, kyomu, n, m);

  lint ans = 0;
  for (int i = 0; i < zembu.size(); i++) {
    lint tmp = 0;
    for (int j = 0; j < q; j++) {
      if (zembu.at(i).at(b.at(j)) - zembu.at(i).at(a.at(j)) == c.at(j))
        tmp += (lint)d.at(j);
    }
    if (tmp > ans) ans = tmp;
  }

  cout << ans << endl;
}