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;

struct StRequir
{
  StRequir() :
    m_nBgn(0), m_nEnd(0), m_nDiff(0), m_nPoint(0) { }

  int m_nBgn;
  int m_nEnd;
  int m_nDiff;
  int m_nPoint;
};

void fnInput(int& rnSeqSiz, int& rnMaxNum, vector<StRequir>& rvoRequir)
{
  int nReqSiz;
  cin >> rnSeqSiz >> rnMaxNum >> nReqSiz;
  rvoRequir.resize(nReqSiz);

  for (StRequir& roRequir : rvoRequir)
    cin >> roRequir.m_nBgn >> roRequir.m_nEnd >> roRequir.m_nDiff >> roRequir.m_nPoint;
}
  
void fnDfsSeqMake(int nPos, int nMaxNum, vector<int>& rvnSeq,
                  const vector<StRequir>& cnrvoRequir, int& rnMaxPoint)
{
  if (nPos == rvnSeq.size())
  {
    int nPoint = 0;

    for (StRequir oRequir : cnrvoRequir)
      if (rvnSeq[ oRequir.m_nEnd - 1 ] - rvnSeq[ oRequir.m_nBgn - 1 ] == oRequir.m_nDiff)
        nPoint += oRequir.m_nPoint;

    rnMaxPoint = max(rnMaxPoint, nPoint);
    return;
  }

  if (nPos > 0)
    rvnSeq[nPos] = rvnSeq[ nPos - 1 ];

  while (rvnSeq[nPos] <= nMaxNum)
  {
    fnDfsSeqMake(nPos + 1, nMaxNum, rvnSeq, cnrvoRequir, rnMaxPoint);
    rvnSeq[nPos]++;
  }
}

int fnMaxPointGet(int nSeqSiz, int nMaxNum, const vector<StRequir>& cnrvoRequir)
{
  int nMaxPoint = 0;
  vector<int> vnSeq(nSeqSiz, 1);

  fnDfsSeqMake(0, nMaxNum, vnSeq, cnrvoRequir, nMaxPoint);
  return nMaxPoint;
}
  
int main()
{
  int nSeqSiz, nMaxNum;
  vector<StRequir> voRequir;

  fnInput(nSeqSiz, nMaxNum, voRequir);
  cout << fnMaxPointGet(nSeqSiz, nMaxNum, voRequir) << endl;

  return 0;
}