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 <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <sstream>
#include <string>
#define _repargs(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define rep(...) _repargs(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define all(x) (x).begin(),(x).end()
#define mod 1000000007
#define inf 2000000007
#define mp make_pair
#define pb push_back
typedef long long ll;
using namespace std;
template <typename T>
inline void output(T a, int p = 0) {
    if(p) cout << fixed << setprecision(p)  << a << "\n";
    else cout << a << "\n";
}
// end of template
struct query {
    int a, b, c, d;
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    // source code
    int N, M, Q;
    cin >> N >> M >> Q;
    vector<query> A(Q);
    rep(i, Q){
        cin >> A[i].a >> A[i].b >> A[i].c >> A[i].d;
        A[i].a--;
        A[i].b--;
    }
    
    vector<int> B(10);
    B[0] = 1;
    int ans = 0;
    rep(b1, 1, 11) rep(b2, b1, 11) rep(b3, b2, 11) rep(b4, b3, 11) rep(b5, b4, 11) rep(b6, b5, 11) rep(b7, b6, 11) rep(b8, b7, 11) rep(b9, b8, 11) {
        B[1] = b1, B[2] = b2, B[3] = b3, B[4] = b4, B[5] = b5, B[6] = b6, B[7] = b7, B[8] = b8, B[9] = b9;
        int tmp = 0;
        rep(i, Q) {
            if(B[A[i].b] - B[A[i].a] == A[i].c) tmp += A[i].d;
        }
        ans = max(ans, tmp);
    }
    output(ans);
    
    
    return 0;
}