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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <string>
#include <iostream>
#include <stack>
#include <queue> // priority_queue も入ってる
#include <set>   // 要素数は size() で取得 multisetもある
#include <map>
#include <array> // sizeはコンパイル時定数で固定
#include <vector>
#include <numeric>   // accumulate, gcd
#include <algorithm> // count_ifに必要
#include <iomanip>   // cout << setprecision(15) << x で小数の出力精度を指定
#include <tuple>
#include <utility> //pair

using namespace std;
// 問題が起こるまでintは使用禁止2020-04-13
using ll = long long;

template <class InputIterator, class T>
bool contains(InputIterator iterator, const T &value)
{
    if (find(iterator.begin(), iterator.end(), value) == iterator.end())
        return false;
    else
        return true;
}

template <class InputIterator>
auto sum(InputIterator iterator)
{
    return accumulate(iterator.begin(), iterator.end(), 0);
}

// =========ここまでテンプレ============

using route = vector<ll>;

int main()
{
    ll n, m, q;
    cin >> n >> m >> q;
    vector<array<ll, 4>> abcds;
    for (ll i = 0; i < q; i++)
    {
        ll a, b, c, d;
        cin >> a >> b >> c >> d;
        --a;
        --b;
        abcds.push_back(array<ll, 4>{a, b, c, d});
    }
    vector<route> routes;
    stack<route> st;

    // DFS初期化
    for (ll i = 1; i < m; i++)
    {
        st.push(vector<ll>{i});
    }

    //DFS実行
    while (!st.empty())
    {
        route rt = st.top();
        st.pop();
        if (rt.size() == n)
        {
            routes.push_back(rt);
        }
        else
        {
            for (ll i = *(--rt.end()); i <= m; i++)
            {
                route r2 = rt;
                r2.push_back(i);
                st.push(r2);
            }
        }
    }

    ll maxScore = 0;

    for (route r : routes)
    {
        ll tempScore = 0;
        for (array<ll, 4> abcd : abcds)
        {
            ll a = abcd[0];
            ll b = abcd[1];
            ll c = abcd[2];
            ll d = abcd[3];

            if (r[b] - r[a] == c)
            {
                tempScore += d;
            }
        }
        maxScore = max(tempScore, maxScore);
    }
    cout << maxScore;
}

// 最大組み合わせ数は19C9 = 92378