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 <bits/stdc++.h>

#define rep(i, s, n) for(int i = s; i < n; ++i)
#define rrep(i, n) for(int i = n - 1; i > -1; --i)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
using namespace std;
const long long INF = 1000000000;
const int MOD = 1000000007;
typedef long long ll;
typedef pair<int, int> P;

int main() {
    ll n, m, q;
    cin >> n >> m >> q;
    vector<vector<ll>> v;
    ll a, b, c, d;
    rep(i, 0, q){
        cin >> a >> b >> c >> d;
        v.push_back({d,a,b,c,0});
    }
    ll ans;
    sort(rall(v));
    rep(i, 0, q){
        int tmpcnt_1 = 0, tmpcnt_2 = 0;
        rep(j, 0, i){
            if(v[j][4] == 1){
                tmpcnt_2++;
                if(v[j][1] <= v[i][1] && v[j][2] >= v[i][2]){
                    if(v[j][3] >= v[i][3]){
                        tmpcnt_1++;
                    }else break;
                }else if(v[j][1] >= v[i][1] && v[j][2] <= v[i][2]){
                    if(v[j][3] <= v[i][3]){
                        tmpcnt_1++;
                    }else break;
                }
            }
        }
        if(tmpcnt_1 == tmpcnt_2){
            ans += v[i][0];
            v[i][4] = 1;
        }
    }
    cout << ans << endl;
}