Problem:
Score : 700 points

Problem Statement

We have N cards numbered 1, 2, ..., N.
Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.
Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

Choose an integer i (1 \leq i \leq N - 1).
Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

1 \leq N \leq 18

1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If it is impossible to have a non-decreasing sequence, print -1.
If it is possible, print the minimum number of operations required to achieve it.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.

Sample Input 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main {
  import java.io.{BufferedReader, InputStream, InputStreamReader}
  import java.util.StringTokenizer
  import scala.reflect.ClassTag

  def main(args: Array[String]): Unit = {
    val out = new java.io.PrintWriter(System.out)
    new Main(out, new InputReader(System.in)).solve()
    out.flush()
  }

  private[this] val oj = System.getenv("MY_DEBUG") == null
  def DEBUG(f: => Unit): Unit = {
    if (!oj){ f }
  }
  def debug(as: Array[Boolean]): Unit = if (!oj){ debug(as.map(x => if(x) "1" else "0").mkString) }
  def debug(as: Array[Int]): Unit = if (!oj){ debug(as.mkString(" ")) }
  def debug(as: Array[Long]): Unit =if (!oj){ debug(as.mkString(" ")) }
  def debugDim(m: Array[Array[Int]]): Unit = if (!oj){
    REP(m.length) { i =>
      debug(m(i))
    }
  }
  def debugDimFlip(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m(0).length) { j =>
      REP(m.length) { i =>
        System.err.print(m(i)(j))
        System.err.print(" ")
      }
      System.err.println()
    }
  }
  def debug(s: => String): Unit = {
    if (!oj){ System.err.println(s) }
  }
  def isDebug[A](debug: => A, online: => A): A = {
    if (oj) online else debug
  }

  class InputReader(val stream: InputStream) {
    private[this] val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private[this] var tokenizer: StringTokenizer = _

    private[this] def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = Integer.parseInt(next())
    def nextLong(): Long = java.lang.Long.parseLong(next())
    def nextChar(): Char = next().charAt(0)

    def ni(): Int = nextInt()
    def nl(): Long = nextLong()
    def nc(): Char = nextChar()
    def ns(): String = next()
    def ns(n: Int): Array[Char] = ns().toCharArray
    def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
    def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
      val A1, A2 = Array.ofDim[Int](n)
      REP(n) { i =>
        A1(i) = ni() + offset
        A2(i) = ni() + offset
      }
      (A1, A2)
    }
    def nm(n: Int, m: Int): Array[Array[Int]] = {
      val A = Array.ofDim[Int](n, m)
      REP(n) { i =>
        REP(m) { j =>
          A(i)(j) = ni()
        }
      }
      A
    }
    def nal(n: Int): Array[Long] = map(n)(_ => nl())
    def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  }

  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }
  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from)(f)
  }
  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }
  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

object Workspace {
  import java.util

  import Main._
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer
  case class Entry(v: Int, i: Int)
  def count(N: Int, E: Array[util.ArrayList[Entry]]): Int = {
    val ix = Array.ofDim[Int](N)
    REP(N) { i =>
      ix(i) = E(i % 2).get(i/2).i
    }
    val bit = new BIT(N)
    var cnt = 0
    REP_r(N) { i =>
      cnt += bit.sum(ix(i))
      bit.add(ix(i), 1)
    }
    cnt
  }

  def _sort(E: util.ArrayList[Entry]): Unit = {
    import java.util.{Collections, Comparator}
    Collections.sort(E, new Comparator[Entry] {
      override def compare(o1: Entry, o2: Entry): Int = {
        if (o1.v == o2.v) {
          Integer.compare(o1.i, o2.i)
        } else {
          Integer.compare(o1.v, o2.v)
        }
      }
    })
  }

  class BIT(n: Int, zero: Int)(f: (Int, Int) => Int) {
    def this(n: Int) = this(n, 0)(_ + _)

    private val N = {
      val a = Integer.highestOneBit(n)
      if (a == n) a else a << 1
    }
    private val bit = if (zero != 0) Array.fill[Int](N + 1)(zero) else Array.ofDim[Int](N + 1)

    /**
      * 1 index
      * addとindex違うよ
      * cumsumなんかといっしょ
      */
    def sum(i: Int): Int = {
      assert(i <= n)
      var x = i
      var s: Int = zero
      while(x > 0) {
        s = f(s, bit(x))
        x -= x & -x
      }
      s
    }

    /**
      * 0 index
      */
    def add(i: Int, a: Int): Unit = {
      assert(i < n)
      var x = i + 1
      while(x <= N) {
        bit(x) = f(bit(x), a)
        x += x & -x
      }
    }

    def sumAll: Int = sum(n)

    // A がLongとかじゃない場合はこれらを実装しないと下の奴らが使えない
    private def sub(a: Int, b: Int) = a - b
    private def lt(a: Int, b: Int) = a < b

    /**
      * [l, r)
      */
    def query(l: Int, r: Int): Int = {
      assert(r > l)
      sub(sum(r), sum(l))
    }

    def lowerBound(W: Int): Int = {
      var k = N
      var x = 0
      var w = W
      while(k > 0) {
        if (x + k <= N && lt(bit(x + k), w)) {
          w = sub(w, bit(x + k))
          x += k
        }
        k /= 2
      }
      math.min(n, x)
    }
  }
}

class Main(out: java.io.PrintWriter, sc: Main.InputReader) {
  import sc._
  import Main._
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer
  import Workspace._

  // toIntとか+7とかするならvalにしろ
  final private[this] val MOD = 1000000007

  def solve(): Unit = {
    val N = ni()
    val A, B = na(N)
    val inf = 1e9.toInt
    var ans = inf
    val oddSize = (N + 1) / 2
    val evenSize = N / 2
    REP(1 << N) { mask =>
      import java.util
      val E = Array.fill[util.ArrayList[Entry]](2)(new util.ArrayList[Entry])
      REP(N) { i =>
        val flip = (mask>>i&1) == 1
        val v = if (flip) B(i) else A(i)
        val x = i % 2 ^ (if (flip) 1 else 0)
        E(x).add(Entry(v, i))
      }

      if (E(0).size == oddSize && E(1).size() == evenSize) {
        _sort(E(0))
        _sort(E(1))
        var ok = true
        var pre = -1
        REP(N) { i =>
          val v = E(i % 2).get(i/2).v
          ok &&= v >= pre
          pre = v
        }
        if (ok) ans = min(ans, count(N, E))
      }
    }

    if (ans == inf) out.println(-1)
    else out.println(ans)
  }
}