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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	N := ReadInt()
	A := ReadInts(N)

	// not coprime
	gcd := A[0]
	for i := 1; i < N; i++ {
		gcd = GCD(gcd, A[i])
	}
	if gcd != 1 {
		fmt.Println("not coprime")
		return
	}

	m := make(map[int]int)
	for i := 0; i < N; i++ {
		factors := Factorization(A[i])
		for _, factor := range factors {
			v := factor[0]
			if m[v] > 0 {
				fmt.Println("setwise coprime")
				return
			}
			m[v] = 1
		}
	}
	fmt.Println("pairwise coprime")
}

func Factorization(n int) [][]int {
	res := [][]int{}
	for i := 2; i*i <= n; i++ {
		if n%i != 0 {
			continue
		}
		cnt := 0
		for n%i == 0 {
			n /= i
			cnt++
		}
		res = append(res, []int{i, cnt})
	}
	if n != 1 {
		res = append(res, []int{n, 1})
	}
	return res
}

func GCD(a, b int) int {
	if b == 0 {
		return a
	}
	return GCD(b, a%b)
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}