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;
using lli = long long;
using pii = pair<int, int>;

#define rep(i,k,n) for(int i=(k); i != int(n); ++i)
#define sz(x) x.size()
#define all(x) x.begin(), x.end()

#define dbg(x) cout << #x << '=' << x << '\n'
#define dbg2(x, y) cout << #x << '=' << x << ' ' << #y << '=' << y << '\n' 

#define input() (*istream_iterator<int>(cin))
#define strin() (*istream_iterator<string>(cin))
#define output(x) cout << x << '\n' 

const int mxq = 60;
int n, m, q;
int mx = 0, cnt = 0;
vector<int> A;
struct quad{
    int a, b, c, d;
};
quad arr[mxq];
void solve(int cur = 1, int sz = 0){
    if(sz == n){
        int sum = 0;
        for(int i = 1; i <= q; ++i){
            cnt++;
            if(A[arr[i].b-1] - A[arr[i].a-1] == arr[i].c) sum += arr[i].d;
        }
        mx = max(sum, mx);
        return;
    }
    for(int i = cur; i <= m; ++i){
        A.push_back(i);
        solve(i, sz+1);
        A.pop_back();
    }
}
int main(){
    ios::sync_with_stdio(false);
    cin >> n >> m >> q;
    for(int i = 1; i <= q; ++i) arr[i] = {input(), input(), input(), input()};
    solve();
    cout << mx;
    return 0;
}