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;

#define int long long

int dp[11][11], n, m, ans = 0;

struct node {
  int a, b, c, d;
  node(){}
  node(int x, int y, int z, int zz) {
    a = x;
    b = y, c = z, d = zz;
  }
};

vector<node> Q;

int get(vector<int> &v) {
  int x = 0;
  for (const auto &[a, b, c, d]: Q) {
    if (v[b] - v[a] == c) x += d;
  }
  return x;
}

void go(int id, int last, vector<int> &v) {
  if (id == n) {
    ans = max(ans, get(v));
    return;
  }
  int ans = 0;  
  for (int i = last; i <= m; ++i) {
    v.push_back(i);
    go(id + 1, i, v);
    v.pop_back();
  }
}

signed main() {
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  // memset(dp, -1, sizeof dp);
  vector<int> v(1);
  int q;
  cin >> n >> m >> q;
  Q.resize(q);
  for (auto &[a, b, c, d]: Q) {
    cin >> a >> b >> c >> d;
  }
  go(0, 1, v);
  cout << ans << '\n';

  return 0;
}