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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/range/adaptor/reversed.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
typedef long long int ll;

#define PI (acos(-1))
#define REP(i,n) for(ll (i)=0;(i)<(n);(i)++)

#define dump(x)  cerr << #x << " = " << (x) << endl;
#define dumparr(x) cerr << #x ; for(auto elem: x){cerr << " " << elem;} cerr << endl;
#define dumppairs(x) cerr << #x ; for(auto elem: x){cerr << "(" << elem.first << " " << elem.second << ") ";} cerr << endl;
#define dumpline cerr << "**********************" << endl;
#define dumpwline(x) cerr << "******** " << #x << "=" << (x) << " ********" << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#define ARRAY_LENGTH(array) (sizeof(array) / sizeof(array[0]))


ll n;
ll m;
ll q;
vector <vector<ll>> qs;

ll calc(vector<ll> num){
    ll last;
    if (!num.empty()){
        last = num[num.size() - 1];
    } else {
        last = 1;
    }
    if (num.size() < n){
        ll ret = 0;
        for(ll last2=last; last2 <= m; last2++){
            vector <ll> num2 = num;
            num2.push_back(last2);
            ret = max(ret, calc(num2));
        }
        return ret;
    }
    ll ret = 0;
    REP(i, q){
        vector<ll> arr = qs[i];
        ll a = arr[0];
        ll b = arr[1];
        ll c = arr[2];
        ll d = arr[3];
        if (num[b-1] - num[a-1] == c){
            ret+=d;
        }
    }
    return ret;
}


int main(void){
    cin >> n;
    cin >> m;
    cin >> q;
    REP(i, q){
        ll a; ll b; ll c; ll d;
        cin >> a >> b >> c >> d;
        qs.push_back({a, b, c, d});
    }
    cout << calc({}) << endl;
    return 0;
}