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;  

typedef pair<long long int,long long int> pa;
 
#define resize(A) A.resize(unique(A.begin(), A.end()) - A.begin())
#define pb push_back
#define  MAX 200005

#define endl "\n"                   //Take care in case of interactive problems


long long int mod=998244353;
long long int MOD=1e9+7;
long long int INF=1e17;
 
 
 
 
////////////////////////////////////////////// sieve  //////////////////////////////////////////////////////////////////
/*
 bool C[MAX];
 
 void sieve()
 {
    long long int i,j;
    for(i=2;i<MAX;i++)
    {
      if(!C[i])
     { 
         
       
        for(j=2*i;j<MAX;j=j+i)
        {
            C[j]=true;
         
        }
      }
        
    }
     
 }*/
 
 
 
 
//////////////////////////////////////////////////////////D-S-U/////////////////////////////////////////////////////////
/*long long int parent[MAX];
long long int size[MAX];
void initialise()
{ //cout<<MAX<<" ";
    for(long  long int i=0;i<MAX;i++)
    {
        parent[i]=i;
        //cout<<i<<" ";
        size[i]=1;
    }
}
long long int  root(long long int x)
{
    while(x!=parent[x])
    {
        parent[x]=parent[parent[x]];
        x=parent[x];
    }
    return x;
}
 
    
void union1(long long int x,long long int y)
{
    if(size[x]>=size[y])
    {
        size[x]+=size[y];
        parent[y]=x;
        
    }
    else
    {
        size[y]+=size[x];
        parent[x]=y;
    }
}*/
//////////////////////////////////////////////////////MODPOWER//////////////////////////////////////////////////////////
 
 
long long int modulo(long long int a,long long  int b, long long int n){
    long long int  x=1, y=a%n; 
    while (b > 0) {
        if (b%2 == 1) {
            x = (x*y) % n; // multiplying with base
        }
        y = (y*y) % n; // squaring the base
        b /= 2;
    }
    return x % n;
}
 
 
////////////////////////////////////////////////BIT/////////////////////////////////////////////////////////////////////
 /*long long int bit[MAX+1]={0};
long long int query(long long int in,long long int n)
{
    //in=in+1;
    long long int sum=0;
    if(in==0)
        return 0;
    while(in>0)
    {
      sum=sum+bit[in];
        
        in=in-(in&(-in));
    }
    return sum;
}
void update(long long int in,long long int n,long long int val)
{
    // in=in+1;
    
    while(in<=n)
    {
       // cout<<in<<" ";
        bit[in]+=val;
        in=in+ (in &(-in));
    }
}
 
 
 
*/
 
//////////////////////////////////////////////// DFS //////////////////////////////////////////////////////////////////
/*
  bool visited[MAX];
 long long int parent[MAX];
 long long int dist[MAX];


void dfs(vector<long long int>adj[],long long int i,long long int k)
{
    visited[i]=true;
    for(auto j:adj[i])
    {
        if(!visited[j])
        {
            dist[j]=dist[i]+1;
            parent[j]=i;
            dfs(adj,j,k);
            
        }
        
    }
}
 */
 

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 

 
 
//long long int R[4]={1,0,-1,0};
//long long int C[4]={0,1,0,-1};
 
 
//NEVER GONNA GIVE YOU UP, NEVER GONNA LET YOU DOWN! 
long long int A[15];
long long int B[15][15];
long long int C[15][15][55];
long long int xr;
void fun(long long int A[],long long int n,long long int i,long long int m,long long int l)
{
    
 //A[i]=l;
   long long int  ans=0;
    for(int i1=1;i1<=n;i1++)
    {
        for(int j1=i1+1;j1<=n;j1++)
        {
            if(A[j1]>=A[i1])
                  ans+=C[i1][j1][A[j1]-A[i1]];
        } 
    }
       if(i==n+1)
       return;

    xr=max(xr,ans);
    for(int j=l;j<=m;j++)
    {
        A[i]=j;
        fun(A,n,i+1,m,j);
    }
    
}

int main()
{
  ios_base::sync_with_stdio(false); 
  cin.tie(NULL);
  cout.tie(NULL);
long long int sum,d,i,w,j,k=0,l=0,r=0,m,n,c,p=0,cnt=0,cnt1=0,x,y=0,z=0,a,b,low,mid,high,ans=0,ans1=0,maxi=0,mini=INF,t1,x1,y1,t,o,i1;
string s,s1,s2,s3;    long long qt,xxx;        char kk,aa,bb,jj;

   
cin>>n>>m>>t;
for(i=0;i<=n;i++)
{
    for(j=0;j<=n;j++)
    {
      
        for(k=0;k<=50;k++)
        C[i][j][k]=0;
    }
}
    while(t--)
    {
        cin>>a>>b>>c>>d;
      
       C[a][b][c]+=d;
    }
   
    for(i=1;i<=n;i++)
    {
        A[i]=1;
    }
    
    
        fun(A,n,1,m,l);
    
    cout<<xr<<endl;
}