Problem:
Score : 300 points

Problem Statement

There are N people, conveniently numbered 1 through N.
They were standing in a row yesterday, but now they are unsure of the order in which they were standing.
However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.
According to their reports, the difference above for person i is A_i.

Based on these reports, find the number of the possible orders in which they were standing.
Since it can be extremely large, print the answer modulo 10^9+7.
Note that the reports may be incorrect and thus there may be no consistent order.
In such a case, print 0.

Constraints

1≦N≦10^5

0≦A_i≦N-1

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the number of the possible orders in which they were standing, modulo 10^9+7.

Sample Input 1

5
2 4 4 0 2

Sample Output 1

4

There are four possible orders, as follows:

2,1,4,5,3

2,5,4,1,3

3,1,4,5,2

3,5,4,1,2

Sample Input 2

7
6 4 0 2 4 0 2

Sample Output 2

0

Any order would be inconsistent with the reports, thus the answer is 0.

Sample Input 3

8
7 5 1 1 7 3 5 3

Sample Output 3

16

Solution in Scala (2.13.1) (judge verdict: Accepted)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}
import java.lang

import scala.annotation.tailrec
import scala.collection.mutable.ArrayBuffer
import scala.reflect.ClassTag

object Main {
  def get[T: ClassTag](implicit in: BufferedReader, converter: String => T): T = {
    converter(in.readLine)
  }

  def getArray[T: ClassTag](implicit in: BufferedReader, converter: String => T): Array[T] = {
    get[String].split("\\s+").map[T](converter)
  }

  implicit val idConverter: String => String = s => s
  implicit val intConverter: String => Int = s => Integer.parseInt(s)
  implicit val longConverter: String => Long = s => lang.Long.parseLong(s)

  def get[T1, T2](
                   implicit in: BufferedReader,
                   converter1: String => T1,
                   converter2: String => T2
                 ): (T1, T2) = {
    getArray[String] match {
      case Array(v1, v2) => (converter1(v1), converter2(v2))
    }
  }

  def get[T1, T2, T3](
                       implicit in: BufferedReader,
                       converter1: String => T1,
                       converter2: String => T2,
                       converter3: String => T3
                     ): (T1, T2, T3) = {
    getArray[String] match {
      case Array(v1, v2, v3) => (converter1(v1), converter2(v2), converter3(v3))
    }
  }

  def get[T1, T2, T3, T4](
                           implicit in: BufferedReader,
                           converter1: String => T1,
                           converter2: String => T2,
                           converter3: String => T3,
                           converter4: String => T4
                         ): (T1, T2, T3, T4) = {
    getArray[String] match {
      case Array(v1, v2, v3, v4) => (converter1(v1), converter2(v2), converter3(v3), converter4(v4))
    }
  }

  implicit class TimesInt(val n: Int) {
    def times(f: Int => Unit): Unit = {
      for (i <- 0 until n) {
        f(i)
      }
    }
  }

  def primes(n: Long): ArrayBuffer[Long] = {
    val buf = ArrayBuffer.empty[Long]
    val s = Math.sqrt(n).toInt

    var v = n
    for (i <- 2 to s) {
      if (v == 1 || v == 0) {
        return buf
      } else {
        while (v % i == 0) {
          buf.append(i)
          v /= i
        }
      }
    }
    if (v > s) {
      buf.append(v)
    }
    buf
  }

  def divisors(n: Int): ArrayBuffer[Int] = {
    val buf = ArrayBuffer.empty[Int]
    val s = Math.sqrt(n).toInt

    for (i <- 1 to s) {
      if (n % i == 0) {
        buf.append(i)
        if (i != n / i) {
          buf.append(n / i)
        }
      }
    }
    buf
  }

  @tailrec
  def gcd(a: Long, b: Long): Long = {
    val reminder = a % b
    if (reminder == 0) {
      b
    } else {
      gcd(b, reminder)
    }
  }

  def lcm(a: Long, b: Long): Long = {
    a / gcd(a, b) * b
  }

  def toBitArray(n: Int, width: Int): Array[Boolean] = {
    val buf = ArrayBuffer.fill(width)(false)

    @tailrec
    def inner(n: Int, i: Int): Array[Boolean] = {
      buf(i) = (n & 1) == 0
      if (i == 0) {
        buf.toArray
      } else {
        inner(n / 2, i - 1)
      }
    }

    inner(n, width - 1)
  }

  def main(args: Array[String]): Unit = {
    implicit val in: BufferedReader = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val n = get[Int]
    val as = getArray[Int].sorted

    val MOD = 1000000007

    out.println(
      if (
        if (n % 2 == 0) {
          @tailrec
          def combiEven(i: Int): Boolean = {
            if (i == n) {
              true
            } else if (i / 2 * 2 + 1 == as(i)) {
              combiEven(i + 1)
            } else {
              false
            }
          }

          combiEven(0)
        } else {
          @tailrec
          def combiOdd(i: Int): Boolean = {
            if (i == n) {
              true
            } else if ((i + 1) / 2 * 2 == as(i)) {
              combiOdd(i + 1)
            } else {
              false
            }
          }

          combiOdd(0)
        }) {
        var prod = 1
        (n / 2).times { _ =>
          prod = prod * 2 % MOD
        }
        prod
      } else {
        0
      }
    )

    out.flush()
  }
}