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)

/*
**   Contest : AtCoder Beginner Contest 165
**   Problem : C - Many Requirements

**    Author : Dhiraj Govindvira
**      Date : 02-May-2020 ~ Saturday
**      Time : 08:39:31 PM
*/

#if __has_include("D:/dhiraj/Programming/debug.h")
    #include "D:/dhiraj/Programming/debug.h"
#else
    #include <bits/stdc++.h>
    using namespace std;
    #define d(...) 11
#endif

// Loops --------------------------------------------------------------------

#define loop(i,s,e)         for(ll i=(s); i<(e); i++)
#define rloop(i,s,e)        for(ll i=(s); i>=(e); i--)
#define iter(it,var)        for(auto it=var.begin(); it!=var.end(); it++)
#define riter(it,var)       for(auto it=var.rbegin(); it!=var.rend(); it++)

// Extra --------------------------------------------------------------------

#define ull                 unsigned long long int
#define ll                  long long int
#define ld                  long double
#define endl                '\n'
#define all(x)              x.begin(),x.end()
#define rall(x)             x.rbegin(),x.rend()

// Template -----------------------------------------------------------------

template <typename T> 
inline bool inrange(T a, T l, T r) {
    if(l>r) swap(l,r);
    return (a>=l and a<=r);
}
template <typename T, typename U> 
inline bool exist(T val, U &any) {
    return (any.find(val) != any.end());
}
// multiple input
template <typename T> 
inline void inp(T &any) {
    cin >> any;
}
template <typename T, typename... U> 
inline void inp(T &a, U &...b) {
    cin >> a; inp(b...);
}
// scan vector
template <typename T> 
inline istream &operator>>(istream &in, vector<T> &a) {
    for(auto &x : a) in >> x;
    return in;
}
// scan pair
template <typename T, typename U> 
inline istream &operator>>(istream &in, pair<T,U> &a) {
    in >> a.first >> a.second; 
    return in;
}

// Solve --------------------------------------------------------------------

void solve(ll &T)
{
    ll n, m, q;
    std::cin>>n>>m>>q;

    vector<ll> a(q), b, c, d;
    b = c = d = a;
    loop(i,0,q) {
        std::cin>>a[i]>>b[i]>>c[i]>>d[i];
        a[i]--, b[i]--;
    }

    vector<ll> A;
    ll ans = 0;
    function<void(int)> dfs = [&](ll val)
    {
        if(A.size()==n)
        {
            d(A);
            ll pt = 0;
            loop(i,0,q) {
                if(A[b[i]]-A[a[i]]==c[i]) {
                    pt += d[i];
                }
            }
            ans = max(ans, pt);
            return;
        }

        loop(i,val,m+1)
        {
            A.push_back(i);
            dfs(i);
            A.pop_back();
        }
    };
    dfs(1);

    std::cout<<ans<<endl;
}

// Main ---------------------------------------------------------------------

int main()
{
    #ifdef Dhiraj
        freopen("D:/dhiraj/Programming/i1.txt","r",stdin);
        freopen("D:/dhiraj/Programming/o1.txt","w",stdout);
    #endif

    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int t = 1;
    loop(i,1,t+1)
    {
        cerr<<"Case #"<<i<<"\n";
        solve(i);
    }
    return 0;
}