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: Wrong Answer)

#include <bits/stdc++.h>
#define REP(i, n) for (decltype(n) i = 0; i < (n); ++i)
using namespace std;
using int64 = long long;

void solve(long long N, long long M, long long Q, std::vector<long long> a,
           std::vector<long long> b, std::vector<long long> c,
           std::vector<long long> d) {
  int64 maxp = 0;
  vector<int64> seq(N, -1);
  function<void(int, int)> search = [&](int i, int val) {
    if (i == N) {
      int64 dsum = 0;
      for (int j = 0; j < Q; ++j) {
        int64 aj = a[j] - 1;
        int64 bj = b[j] - 1;
        if (seq[bj] - seq[aj] == c[j]) {
          dsum += d[j];
        }
      }
      if (maxp < dsum) {
        maxp = dsum;
      }
      return;
    }
    seq[i] = val;
    for (int j = val; j <= 10; ++j) {
      search(i + 1, j);
    }
  };
  search(0, 1);
  cout << maxp << endl;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long N;
  scanf("%lld", &N);
  long long M;
  scanf("%lld", &M);
  long long Q;
  scanf("%lld", &Q);
  std::vector<long long> a(Q);
  std::vector<long long> b(Q);
  std::vector<long long> c(Q);
  std::vector<long long> d(Q);
  for (int i = 0; i < Q; i++) {
    scanf("%lld", &a[i]);
    scanf("%lld", &b[i]);
    scanf("%lld", &c[i]);
    scanf("%lld", &d[i]);
  }
  solve(N, M, Q, std::move(a), std::move(b), std::move(c), std::move(d));
}