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 <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#define _GLIBCXX_DEBUG
#define INF 100000010
using namespace std;
const int mod = 1000000007;


int main(){
int64_t N,M,Q,sum=0,ans=0;
  cin>>N>>M>>Q;
  vector<vector<int> > A(Q,vector<int>(4));
  vector<int> B(11,1);
  for(int i=0; i<Q; i++){
    for(int j=0; j<4; j++){
      cin>>A[i][j];
    }
  }
  for(int i1=1; i1<=10; i1++){B[1]=i1;
  for(int i2=i1; i2<=10; i2++){B[2]=i2;
  for(int i3=i2; i3<=10; i3++){B[3]=i3;
  for(int i4=i3; i4<=10; i4++){B[4]=i4;
  for(int i5=i4; i5<=10; i5++){B[5]=i5;
  for(int i6=i5; i6<=10; i6++){B[6]=i6;
  for(int i7=i6; i7<=10; i7++){B[7]=i7;
  for(int i8=i7; i8<=10; i8++){B[8]=i8;
  for(int i9=i8; i9<=10; i9++){B[9]=i9;
  for(int i10=i9; i10<=10; i10++){B[10]=i10;
  sum=0;
  for(int i=0; i<Q; i++){
    if(B[A[i][1]]-B[A[i][0]]==A[i][2]){sum+=A[i][3];}
    if(i==Q-1){ans=max(ans,sum);}
  }
  }
  }
  }
  }
  }
  }
  }
  }
  }
  }
  cout << ans << endl;
}