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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long int
#define pb push_back
#define N 200100
#define mod 1000000007
#define MOD 998244353
#define fn(i,n) for(int i=0;i<n;i+=1)
#define rep(i,l,r) for(int i=l;i<=r;i+=1)
#define INF 100000000000000000
#define pii pair<int,int>
#define speed ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
struct Node{
	int a,b,c,d;
}Q[52];
bool fun(Node al,Node bl){
	return al.d>bl.d;
}
signed main()
{
    
    speed
    int n,m,q;
    cin>>n>>m>>q;
    vector <int> A(n+1,0);
    vector<int> vis(n+1,0);
    for(int i=1;i<=q;i++){
    	cin>>Q[i].a>>Q[i].b>>Q[i].c>>Q[i].d;
    }
    sort(Q+1,Q+1+q,fun);
    int su=0;
    for(int i=1;i<=q;i++){
    	int e=Q[i].a;
    	int f=Q[i].b;
    	int g=Q[i].c;
    	int h=Q[i].d;
    	if(e>f)swap(e,f);
    	if(A[e]==0 && A[f]==0){
    		su+=h;
    		A[e]=1;A[f]=g+1;
    	}
    	else if(A[e]!=0 && A[f]==0){
    		A[f]=g+A[e];
    		su+=h;
    	}
    	else if(A[e]==0 && A[f]!=0){
    		A[e]=A[f]-g;
    		su+=h;
    	}
    	else{
    		if(A[f]-A[e]==g){
    			su+=h;
    		}
    	}
    }
    cout<<su<<endl;
   
    



    

    

 
    return 0;
}