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: Accepted)

import scala.io.StdIn._

object Helpers {
  def readIntLine = readLine.split(" ").map(_.toInt)
  def readInts(n: Int) = Array.fill(n)(readInt)

  def splitDigits(i: Int): Seq[Int] = i.toString.map(_.asDigit)

  def log[A](x: A): A = {println(x); x}

  implicit class IntImplicits(val i: Int) {
    def isEven = i % 2 == 0
    def isOdd = !isEven

    def ** (exp: Int): Int = scala.math.pow(i, exp).intValue
  }

  implicit class LongImplicits(val i: Long) {
    def isEven = i % 2 == 0
    def isOdd = !isEven

    def ** (exp: Long): Long = scala.math.pow(i, exp).longValue
  }
}

object Main extends App {
  import Helpers._

  val Array(n, m, q) = readIntLine
  val as = for (_ <- 0 until q) yield readIntLine

  def mycomb[T](n: Int, l: List[T]): List[List[T]] =
    n match {
      case 0 => List(List())
      case _ => for(el <- l;
                sl <- mycomb(n-1, l dropWhile { _ != el } ))
                yield el :: sl
  }
  
  def comb[T](n: Int, l: List[T]): List[List[T]] = mycomb(n, l.distinct)

  val candidate = comb(n, (1 to m).toList)

  println((for {
    x <- candidate
  } yield (for {
    a <- as
    if x(a(1) - 1) - x(a(0) - 1) == a(2)
  } yield a(3)).sum).max)
}