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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            /* 階乗
            for (int i = 0; i < 10; i++)
            {
                WriteLine("{0} : {1}",i,Factorial(i));
            }
            */

            /* 最大公約数（ユーグリッド互換法）
            var a = 630;var b = 300;
            WriteLine("{0} {1} => {2}", a, b, Gcd(a, b));
            */

            /* 累乗（バイナリ法）
            for (int i = 0; i < 10; i++)
            {
                WriteLine("{0} : {1}", i, Power(i,i));
            }
            */

            var N = cin.ReadInt;
            var M = cin.ReadInt;
            //var list = GetArrays(new List<int[]> { new int[] { } }, 1, N, M);

            //Func<List<int[]>, List<int[]>, int> GetArrayFunc = null;
            Func<List<int[]>, int ,List<int[]>> GetArraysFunc = null;
            GetArraysFunc = (List<int[]> list,int n) =>
            {
                if (n > N) return list;
                var newlist = new List<int[]>();
                foreach (var item in list)
                {
                    int start = n == 1 ? 1 : item[n - 2];
                    for (int i = start; i <= M; i++)
                    {
                        newlist.Add(item.Concat(new int[] { i }).ToArray());
                    }
                }
                return GetArraysFunc(newlist, n + 1);
            };

            var list = GetArraysFunc(new List<int[]> { new int[] { } },1);

            var Q = cin.ReadInt;
            var a = new int[Q];
            var b = new int[Q];
            var c = new int[Q];
            var d = new int[Q];

            for (int i = 0; i < Q; i++)
            {
                a[i] = cin.ReadInt;
                b[i] = cin.ReadInt;
                c[i] = cin.ReadInt;
                d[i] = cin.ReadInt;
            }

            var ans = 0;

            foreach (var item in list)
            {
                var sum = 0;
                for (int i = 0; i < Q; i++)
                {
                    if (item[b[i] - 1] - item[a[i] - 1] == c[i]) sum += d[i];
                }
                if (sum > ans) ans = sum;
            }

            WriteLine(ans);
        }

        public List<int[]> GetArrays(List<int[]> list, int n, int N, int M)
        {
            if (n > N) return list;
            var newlist = new List<int[]>();
            foreach (var item in list)
            {
                int start = n == 1 ? 1 : item[n - 2];
                for (int i = start; i <= M; i++)
                {
                    newlist.Add(item.Concat(new int[] { i }).ToArray());
                }
            }
            return GetArrays(newlist, n + 1, N, M);
        }

        public int Power(int a, int n)
        {
            if (n == 0) return 1;
            var b = Power(a, n / 2);
            b *= b;
            if (n % 2 == 1) b *= a;
            return b;
        }

        public int Gcd(int a, int b)
        {
            if (b == 0) return Math.Abs(a);
            return Gcd(b, a % b);
        }

        public int Factorial(int n)
        {
            if (n == 0) return 1;
            return n * Factorial(n - 1);
        }

        public void Display(int[] array, int index)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item.ToString();
            }
            WriteLine("{0} : {1}", index, txt);
        }
    }


    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; i++)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }


        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}