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)

#include<bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define tp tuple<int,int,int>
#define mtp make_tuple
using namespace std;

const int N=55;
int n,m,q,a[N],b[N],c[N],d[N],res,now[N];

void backtrack(int i)
{
    if(i>n)
    {
        int cost=0;
        for(int j=1;j<=q;j++) if(now[b[j]]-now[a[j]]==c[j]) cost+=d[j];
        res=max(res,cost);
        return ;
    }
    for(int j=max(1ll,now[i-1]);j<=m;j++)
    {
        now[i]=j;
        backtrack(i+1);
    }
}

main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin>>n>>m>>q;
    for(int i=1;i<=q;i++) cin>>a[i]>>b[i]>>c[i]>>d[i];
    backtrack(1);
    cout<<res;
}