Problem:
Score : 500 points

Problem Statement

We have N integers. The i-th number is A_i.

\{A_i\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\{A_i\} is said to be setwise coprime when \{A_i\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \{A_i\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

2 \leq N \leq 10^6

1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

If \{A_i\} is pairwise coprime, print pairwise coprime; if \{A_i\} is setwise coprime, print setwise coprime; if neither, print not coprime.

Sample Input 1

3
3 4 5

Sample Output 1

pairwise coprime

GCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.

Solution in Scala (2.13.1) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt()
  val as = List.fill(n)(sc.nextLong())
  val m = 1000000

  def divisors(n: Int): Array[Int] = {
    val divisors = Array.fill(n+1)(0)
    for (i <- 2 to n if divisors(i) == 0) {
      var k = 1
      while (i * k <= n) {
        if (divisors(i * k) == 0) {
          divisors(i * k) = i
        }
        k += 1
      }
    }
    divisors
  }

  val divisor = divisors(m)

  def primeFactors(n: Int, res: IndexedSeq[Int] = IndexedSeq()): IndexedSeq[Int] = {
    if (n == 1) {
      res
    } else {
      val d = divisor(n)
      if (d == n) {
        res :+ n
      } else {
        var m = n
        var res2 = res
        while (m % d == 0) {
          m /= d
          res2 :+= d
        }
        primeFactors(m, res2)
      }
    }
  }

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

  val exist = Array.fill(m+1)(false)
  var pair = true
  as.map(a => primeFactors(a.toInt)).foreach(fs =>
    for (f <- fs.distinct) {
      if (exist(f)) {
        pair = false
      } else {
        exist(f) = true
      }
    }
  )

  if (pair) {
    println("pairwise coprime")
  } else if (as.reduceLeft[Long]{case (x, y) => gcd(x, y)} == 1) {
    println("setwise coprime")
  } else {
    println("not coprime")
  }
}