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 <iostream>
#include <algorithm>
#include <vector>
#include <deque>
#include <queue>
#include <set>
#include <map>
#include <limits>
#include <cmath>
#include <iomanip>
#include <functional>
#include <random>
#include <boost/multiprecision/cpp_int.hpp>

using namespace std;
using ll = long long;
namespace mp = boost::multiprecision;
ll BASE_NUM = 1000000007;

int solve(vector<ll> &candidate, vector<vector<ll>> &Qs, ll N, ll M)
{
  if (candidate.size() == N)
  {
    ll value = 0;
    for(auto q:Qs){
      if (candidate[q[1]-1] - candidate[q[0]-1] == q[2]){
        value += q[3];
      }
    }
    return value;
  }
  else
  {
    ll max_value = 0;
    for (int i = candidate.back(); i <= M; i++)
    {
      candidate.push_back(i);
      ll value = solve(candidate,Qs,N,M);
      max_value = max(max_value,value);
      candidate.pop_back();
    }
    return max_value;
  }
}

int main()
{
  // 整数の入力

  ll N, M, Q;
  cin >> N >> M >> Q;
  vector<vector<ll>> Qs;
  for (int i = 0; i < Q; i++)
  {
    ll a, b, c, d;
    cin >> a >> b >> c >> d;
    Qs.push_back({a, b, c, d});
  }
  vector<ll> candidate = {1};
  cout << solve(candidate,Qs,N,M) << endl;
  return 0;
}