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 Go (1.14.1) (judge verdict: Accepted)

package main
import (
  "bufio"
  "os"
  "strconv"
  "strings"
  "fmt"
)

func Count(R *[][]int, A *[]int, ans *int, N, M, i int) {
  if i <= N {
    for a := (*A)[i - 1]; a <= M; a++ {
      (*A)[i] = a
      Count(R, A, ans, N, M, i + 1)
    }
  } else {
    cnt := 0
    for _, r := range (*R) {
      if (*A)[r[1]] - (*A)[r[0]] == r[2] { cnt += r[3] }
    }
    (*ans) = MaxInt(cnt, (*ans))
  }
}

func Solve() {
  var N, M, Q int
  NextInt(&N, &M, &Q)
  R := make([][]int, Q)
  for i := range R { NextIntVec(&R[i]) }
  A := make([]int, N + 1)
  A[0] = 1
  ans := 0
  Count(&R, &A, &ans, N, M, 1)
  Write(ans)
}

func main() {
  Solve()
  Output()
}

var reader = bufio.NewReaderSize(os.Stdin, 1000000)
var writer = bufio.NewWriter(os.Stdout)
func NextLine() string {
  buffer := make([]byte, 0)
  for true {
    line, isPrefix, err := reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer, line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func NextInt(A ...*int) {
  L := strings.Split(NextLine(), " ")
  for i, a := range A {
    *a, _ = strconv.Atoi(L[i])
  }
}
func NextIntVec(A *[]int) {
  L := strings.Split(NextLine(), " ")
  (*A) = make([]int, len(L))
  for i, l := range L {
    (*A)[i], _ = strconv.Atoi(l)
  }
}
func NextFloat(A ...*float64) {
  L := strings.Split(NextLine(), " ")
  for i, a := range A {
    *a, _ = strconv.ParseFloat(L[i], 64)
  }
}
func NextFloatVec(A *[]float64) {
  L := strings.Split(NextLine(), " ")
  (*A) = make([]float64, len(L))
  for i, l := range L {
    (*A)[i], _ = strconv.ParseFloat(l, 64)
  }
}
func Write(s interface{}) {
  fmt.Fprintln(writer, s)
}
func WriteIntVec(A []int) {
  S := make([]string, len(A))
  for i, a := range A {
    S[i] = strconv.Itoa(a)
  }
  Write(strings.Join(S, " "))
}
func Output() {
  _ = writer.Flush()
}
func MaxInt(A ...int) int {
  max := A[0]
  for _, a := range A {
    if max < a { max = a }
  }
  return max
}
func MinInt(A ...int) int {
  min := A[0]
  for _, a := range A {
    if a < min { min = a }
  }
  return min
}
func SumInt(A ...int) int {
  sum := 0
  for _, a := range A {
    sum += a
  }
  return sum
}
func AbsInt(x int) int {
  if x < 0 { x = -x }
  return x
}