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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

int main() {
    int n,m,q;
    cin >> n >> m >> q;
    vector<int> a(q);
    vector<int> b(q);
    vector<int> c(q);
    vector<int> d(q);
    for (int i=0; i<q; i++)
        cin >> a[i] >> b[i] >> c[i] >> d[i];

    vector<int> vec(10);
    ll ans = 0;
    for (int x1=1; x1<=m; x1++) {
        vec[0] = x1;
        for (int x2=x1; x2<=m; x2++) {
            vec[1] = x2;
            for (int x3=x2; x3<=m; x3++) {
                vec[2] = x3;
                for (int x4=x3; x4<=m; x4++) {
                    vec[3] = x4;
                    for (int x5=x4; x5<=m; x5++) {
                        vec[4] = x5;
                        for (int x6=x5; x6<=m; x6++) {
                            vec[5] = x6;
                            for (int x7=x6; x7<=m; x7++) {
                                vec[6] = x7;
                                for (int x8=x7; x8<=m; x8++) {
                                    vec[7] = x8;
                                    for (int x9=x8; x9<=m; x9++) {
                                        vec[8] = x9;
                                        for (int x10=x9; x10<=m; x10++) {
                                            vec[9] = x10;
                                            ll sum = 0;
                                            for (int i=0; i<q; i++) {
                                                if (vec[b[i]-1] - vec[a[i]-1] == c[i])
                                                    sum += d[i];
                                            }
                                            ans = max(ans, sum);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
    cout << ans << endl;

    return 0;
}