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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define ll          long long
#define pb          push_back
#define eb 			emplace_back
#define mp 			make_pair
#define pii         pair<ll,ll>
#define vi          vector<ll>
#define vii         vector<pii>
#define mi          map<ll,ll>
#define mii         map<pii,ll>
#define all(a)      (a).begin(),(a).end()
#define fi          first
#define si          second
#define sz(x)       (ll)x.size()
#define endl        '\n'
#define checkbit(n, b) ((n >> b) & 1)
#define mod        1000000007
#define inf        1000000000000000000
#define puts(n)		cout<<n;
#define rep(i,a,b)  for(ll i=a;i<b;i++)
#define setbits(x) __builtin_popcount(x)
#define mset(m,v) memset(m,v,sizeof(m))
using namespace std;
ll n,m,q;
ll a[50],b[50],c[50],d[50];
ll ans=0;
void dfs(vi s){
	if(s.size()>=n){
		ll val=0;
		for(ll i=0;i<q;i++){
			if(s[b[i]] - s[a[i]]==c[i]) val+=d[i];
		}
		ans=max(ans,val);
		return ;
	}
	for(ll i=s.back();i<=m;i++){
		vi tmp(s.begin(),s.end());
		tmp.pb(i);
		dfs(tmp);
	}
}
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	cin>>n>>m>>q;
	for(ll i=0;i<q;i++){
		cin>>a[i]>>b[i]>>c[i]>>d[i];
		a[i]--;
		b[i]--;
	}
	vi s;
	s.pb(1);
	dfs(s);
	cout<<ans;
	return 0;
}