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 <map>
#include <set>
#include <list>
#include <cmath>
#include <deque>
#include <stack>
#include <queue>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <random>
#include <chrono>
#include <utility>
#include <numeric>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <sstream>
#include <assert.h>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <unordered_map>
using namespace std;

void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(bool x) {cerr << (x ? "true" : "false");}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}

template<typename T, typename V> void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i : x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";} void _print() {cerr << "]\n";}
template <typename T, typename... V>void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef HOME
#warning CHECK int:ll::INT_MAX:LLONG_MAX
#define maxn 20
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define maxn 2000006
#define gcd __gcd
#define debug(x...)
#endif

#define ff first
#define endl '\n'
#define ss second
#define inf 0x3f3f3f3f
#define MOD 1000000007
#define PI 3.14159265358979323846264338327950L
#define f(i,x,n) for(int i=x;i<=n;i++)
#define fr(i,x,n) for(int i=x;i>=n;i--)
struct _ { ios_base::Init i; _() { ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL); } } _;

int dx[] = { -1, 0, 1, 0, -1, -1, 1, 1};
int dy[] = {0, 1, 0, -1, -1, 1, 1, -1};

long long  n, m, q, ans;
vector<vector<long long >> quad;

void func(long long  i, long long  prev, vector<long long > num) {
	if (i == n) {
		long long  curr = 0;
		for (auto i : quad) {
			if (num[i[1] - 1] - num[i[0] - 1] == i[2]) curr += i[3];
		}
		ans = max(ans, curr);
		return;
	}

	if (prev == 10) return;

	for (long long  dig = prev; dig <= m; dig++) {
		num.push_back(dig);
		func(i + 1, dig, num);
		num.pop_back();
	}

	return;
}

int  main() {

	cin >> n >> m >> q;
	quad.resize(q, vector<long long >(4, 0));
	for (long long  i = 0; i <= q - 1; i++) for (long long  j = 0; j <= 3; j++) cin >> quad[i][j];
	func(0, 0, vector<long long >());

	cout << ans;

	return 0;
}