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<vector>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<deque>
#include<map>
#include<bitset>
using namespace std;

typedef long long ll;
#define rep(i, n) for(int i = 0;i < (n);i++)
#define repr(i, n) for(int i = (n);i >= 0;i--)
#define repf(i, m, n) for(int i = (m);i < (n);i++)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1;} return 0;}
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1;} return 0;}
int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};
//////////////////////////////////////////////////


int main() {
    int n, m, q; cin >> n >> m >> q;
    vector<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]--;
    }

    int ans = 0;
    vector<int> k(n+1);
    auto rec = [&](auto &&rec, int v, int pos) -> void {
        if (pos == n) {
            // rep(i,n) {
            //     cout << k[i] << " ";
            // }
            // cout << endl;
            int tmp = 0;
            rep(i,q) {
                if (k[b[i]] - k[a[i]] == c[i]) tmp += d[i];
            }
            chmax(ans, tmp);
            return;
        }

        repf(i,v,m+1) {
            k[pos] = i;
            rec(rec, i, pos+1);
        }
    };

    rec(rec, 1, 0);
    cout << ans << endl;

    return 0;
}