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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
namespace Atcoder_0404
{
    class Program
    {
        public class InputSet
        {


            public int a;
            public int b;
            public int c;
            public int d;

            public InputSet(int[] data)
            {
                a = data[0];
                b = data[1];
                c = data[2];
                d = data[3];
            }
        }

        public class InputPair
        {
            public List<InputSet> list = new List<InputSet>();
            public int sum = 0;
            public InputPair(List<InputSet> pair)
            {
                list = pair;
                foreach(var data in list)
                {
                    sum += data.d;
                }
            }
        }

        static void Main(string[] args)
        {
            var NMQ = GetInput_int();
            var _Acount = NMQ[0];
            var _Amax = NMQ[1];
            var _pearCount = NMQ[2];
            List<InputSet> _setList = new List<InputSet>();
            for(int i = 0; i < _pearCount; i++)
            {
                var pair = GetInput_int();
                _setList.Add(new InputSet(pair));
            }
            Stack<int> _checkSet = new Stack<int>();
            for(int i = 0; i < _Acount; i++)
            {
                _checkSet.Push(1);
            }
            long sumMax = 0;
            while (true)
            {
                long sum = 0;
                var tempqueue = new List<int>(_checkSet);
                tempqueue.Reverse();
                foreach (var check in _setList)
                {
                    if (tempqueue[check.b-1] - tempqueue[check.a-1] == check.c)
                    {
                        sum += check.d;
                    }
                }
                if (sum > sumMax)
                {
                    sumMax = sum;
                }

                while (true)
                {
                    if (_checkSet.Count == 0) break;
                    var check = _checkSet.Pop();
                    check++;
                    if (check > _Amax)
                    {

                    }
                    else
                    {
                        while (_checkSet.Count < _Acount)
                        {
                            _checkSet.Push(check);
                        }
                        break;
                    }
                }
                if (_checkSet.Count == 0) break;
            }

            Console.WriteLine(sumMax);
            GetInput_string();

            
        }
        #region input
        

        static string[] GetInput_string()
        {
            var input = Console.ReadLine().Split(' ');
            return input;
        }

        static int[] GetInput_int()
        {
            var input = GetInput_string();
            var result = new int[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = int.Parse(input[i]);
            }
            return result;
        }
        static long[] GetInput_long()
        {
            var input = GetInput_string();
            var result = new long[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = long.Parse(input[i]);
            }
            return result;
        }
        #endregion
        #region sonota
        static void Swap_array<T>(T[] target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        static void Swap_list<T>(List<T> target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        /// <summary>
        /// 最大公約数
        /// </summary>
        public static int GCD(int a, int b)
        {

            /* 自然数 a > b を確認・入替 */
            if (a < b)
            {
                int tmp = a;
                a = b;
                b = tmp;
            }

            /* ユークリッドの互除法 */
            int r = a % b;
            while (r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }
            return b;
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        public static int LCM(int a, int b)
        {
            int x = a * b;
            b = GCD(a, b);
            return x / b;

        }
        #endregion

        static long mod = 1000000000 + 7;
    }
}