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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <stdio.h>

#include <algorithm>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <utility>
#include <vector>

using namespace std;
typedef long long llong;

// returns false when it is last combination
static bool Next(vector<int>& x, int M) {
  int p = x.size() - 1;
  if (x[p] < M) {
    ++x[p];
    return true;
  }
  x[p] = 1;
  --p;
  while (p >= 0) {
    if (x[p] < M) {
      int t = ++x[p];
      for (int j = p + 1; j < x.size(); ++j) {
        if (x[j] < t)
          x[j] = t;
      }
      return true;
    }
    --p;
  }
  return false;
}

void CManyRequirements(std::istream& in, std::ostream& out) {
  int N, M, Q;
  in >> N >> M >> Q;
  vector<vector<int>> v(Q);
  for (int i = 0; i < Q; ++i) {
    v[i].resize(4);
    in >> v[i][0] >> v[i][1] >> v[i][2] >> v[i][3];
  }

  vector<int> a(N);
  fill(a.begin(), a.end(), 1);
  llong max_score = 0;
  do {
    llong score = 0;
    for (int i = 0; i < Q; ++i) {
      if (a[v[i][1] - 1] - a[v[i][0] - 1] == v[i][2])
        score += v[i][3];
    }
    max_score = max(max_score, score);
  } while (Next(a, M));
  out << max_score << "\n";
}

int main(int argc, char** argv) { CManyRequirements(cin, cout); return 0; }