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 Scala (2.13.1) (judge verdict: Wrong Answer)

import scala.util.control.Breaks

object Main extends App {
  val nmq =  scala.io.StdIn.readLine()
  val nmqArray = nmq.split(" ").map(_.toInt).toSeq
  val n = nmqArray(0)
  val m = nmqArray(1)
  val q = nmqArray(2)

  var abcdVector = Vector.empty[Vector[Int]]
  (1 to q).foreach { _ =>
    val a =  scala.io.StdIn.readLine()
    abcdVector :+= a.split(" ").map(_.toInt).toVector
  }
  val max = abcdVector.map(a => a(3)).sum
  var tempMax = 0

  def getInitialAArray(): scala.collection.mutable.Seq[Int] = {
    var returnSeq = scala.collection.mutable.Seq.empty[Int]
    (1 to n).foreach { _=>
      returnSeq :+= 1
    }
    returnSeq
  }
  var aSeq = getInitialAArray()

  val break = new Breaks
  break.breakable {
    (0 to n - 1).foreach { i =>
      kensyou(i)
    }

    def kensyou(index: Int): Unit = {
      if(index == 0) {
        (1 to m).foreach { i =>
          aSeq(n - 1) = i
          calc(aSeq)
        }
      } else {
        (1 to m).foreach { i =>
          aSeq(n - 1 - index) = i
          kensyou(index - 1)
        }
      }
    }

    def calc(kensyouArray: scala.collection.mutable.Seq[Int]) = {
      var tempCalc = 0
      abcdVector.foreach { abcd =>
        if (kensyouArray(abcd(1) - 1) - kensyouArray(abcd(0) - 1) == abcd(2)) {
          tempCalc = tempCalc + abcd(3)
        }
      }

      if(tempCalc == max) {
        tempMax = tempCalc
        break.break()
      } else if(tempCalc > tempMax) {
        tempMax = tempCalc
      }
    }
  }

  println(tempMax)
}