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>
#include<cctype>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define reps(i,n) for (int i=1;i<=(n);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rreps(i,n) for (int i=(n);i>0;i--)
#define all(v) (v).begin(),(v).end()
#define pi 3.1415926535897932384
#define E9 1000000000
#define eps 1e-4
#define pii pair<int,int>
template<class T> inline bool chmin(T &a, T b) {if (a>b) {a = b; return 1;} return 0;};
template<class T> inline bool chmax(T &a, T b) {if (a<b) {a = b; return 1;} return 0;};
typedef long long int ll;
const long long INF = 1LL << 60;


int main(){
  int N, M, Q; cin >> N >> M >> Q;
  int a[Q], b[Q], c[Q], d[Q];
  rep(i,Q) {
    cin >> a[i] >> b[i] >> c[i] >> d[i];
    --a[i], --b[i];
  }

  vector<vector<int>> U;

  queue<vector<int>> q;
  reps(i,M) q.push(vector<int>(1,i));

  while (!q.empty()){
    auto vec = q.front(); q.pop();
    // cout << vec.size() << endl;
    if (vec.size()==N) {
      U.push_back(vec);
      continue;
    }
    int l = vec.back();
    for (int j=l;j<=M;j++){
      auto vec_c = vec;
      vec_c.push_back(j);
      q.push(vec_c);
    }
  }


  ll ans = 0;
  for (auto vec : U){
    ll tmp = 0;
    rep(i,Q){
      if (vec[b[i]] - vec[a[i]]==c[i]) tmp += d[i];
    }
    chmax(ans, tmp);
  }
  cout << ans << endl;
  
  // cout << fixed << setprecision(10);
  
  return 0;
}