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 5.4.1) (judge verdict: Wrong Answer)

#include<algorithm>
#include<bitset>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<map>
#include<iostream>
#include<queue>
#include<set>
#include<stack>
#include<string>
#include<vector>
using namespace std;
#define ll long long
#define f(i,a,b) for(int i=a;i<=b;i++)
inline ll read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
#define d read()
ll n,m,q,ans;
ll a[15],b[15],c[15],dd[15];
ll sq[15];
void dfs(ll u,ll st){
	if(u==n+1){
		ll k=0;
		f(i,1,q)if(sq[b[i]]-sq[a[i]]==c[i])k+=dd[i];
		ans=max(ans,k);
		return;
	}
	f(i,st,m)sq[u]=i,dfs(u+1,i);
}
int main(){
	n=d,m=d,q=d;
	f(i,1,q)a[i]=d,b[i]=d,c[i]=d,dd[i]=d;
	dfs(1,1);
	cout<<ans;
	return 0;
}