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)

/*
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                                                     P_r_A_d_Y
*/
#include<bits/stdc++.h>
using namespace std;
#define int long long int
#define endl "\n"
#define mod 1000000007
#define inf 1e18
const int N = 300005;
#define fastIO ios_base::sync_with_stdio(false); cin.tie(NULL);
void cs(int &x)
{
    cout << "Case #" << x << ": ";
}
bool cmp(string a, string b)
{
    return a + b < b + a;
}
int n,m,q,ans=0;
vector<vector<int>>qw;
vector<int>v;
void help(int i,int val)
{
    if(i==n)
    {
        int cnt=0;
        for(int j=0;j<q;j++)
        {
            if(v[qw[j][1]-1]-v[qw[j][0]-1]== qw[j][2])
                cnt+=qw[j][3];
        }

        ans=max(ans,cnt);
        return ;
    }


    for(int p=val;p<=m;p++)
    {
        v[i]=p;
        help(i+1,p);
    }


}
int32_t main()
{
    fastIO;
    // int t; cin >> t;
    // int x = 1;
    // while (t--)
    // {

        cin>>n>>m>>q;
        qw.resize(q,vector<int>(4));
        v.resize(n);

        for(int i=0;i<q;i++)
        {
            cin>>qw[i][0]>>qw[i][1]>>qw[i][2]>>qw[i][3];
        }

        help(0,1);
        cout<<ans<<endl;

    //}
    return 0;
}