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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
  public void Solve()
  {
    var (N, M, Q) = Cin<int, int, int>();
    var qs = new (int, int, int, int)[Q];
    for (int i = 0; i < Q; ++i)
    {
      var (a, b, c, d) = Cin<int, int, int, int>();
      qs[i] = (a - 1, b - 1, c, d);
    }
    for (int i = 1; i <= M; ++i)
    {
      var l = new List<int>();
      l.Add(i);
      dfs(l, 1, N, M, qs);
    }
    Write(kotae);

  }

  long kotae = 0;
  void dfs(List<int> lis, int depth, int N, int M, (int, int, int, int)[] qs)
  {
    if (depth == N)
    {
      long ans = 0;
      for (int i = 0; i < qs.Length; ++i)
      {
        if (lis[qs[i].Item2] - lis[qs[i].Item1] == qs[i].Item3) ans += qs[i].Item4;
      }
      kotae = Max(kotae, ans);
      return;
    }
    for (int i = lis.Last(); i <= M; ++i)
    {
      var ll = lis.ToList();
      ll.Add(i);
      dfs(ll, depth + 1, N, M, qs);
    }
    return;
  }

}



public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b)
  {
    if (a < b) return GCD(b, a);
    while (b != 0)
    {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = n; i >= n - r + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long n, long r)
  {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
}
public static class Utils
{
  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(string N)
  {

    int ret = 0;
    for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }


  public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
  public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
  public static T Cast<T>(string s)
  {
    if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
    else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
    else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
    else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
    else return ConvertType<T, string>(s);
  }
  public static T Cin<T>() { var t = Strs; return (Cast<T>(t[0])); }
  public static (T, U) Cin<T, U>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1])); }
  public static (T, U, V) Cin<T, U, V>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2])); }
  public static (T, U, V, W) Cin<T, U, V, W>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3])); }
  public static (T, U, V, W, X) Cin<T, U, V, W, X>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4])); }
  public static (T, U, V, W, X, Y) Cin<T, U, V, W, X, Y>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5])); }
  public static (T, U, V, W, X, Y, Z) Cin<T, U, V, W, X, Y, Z>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5]), Cast<Z>(t[6])); }
}