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"
	"sort"
	"strconv"
)

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getInts(N int) []int {
	ret := make([]int, N)
	for i := 0; i < N; i++ {
		ret[i] = getInt()
	}
	return ret
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

// min, max, asub, absなど基本関数
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func asub(a, b int) int {
	if a > b {
		return a - b
	}
	return b - a
}

func abs(a int) int {
	if a >= 0 {
		return a
	}
	return -a
}

func lowerBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] >= x
	})
	return idx
}

func upperBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] > x
	})
	return idx
}

var pfs map[int]int

// PfsMap : 素因数分解し、マップを作成
func PfsMap(n int) bool {
	for n%2 == 0 {
		pfs[2] = pfs[2] + 1
		// if pfs[2] == 2 {
		// 	return false
		// }
		n = n / 2
		for n%2 == 0 {
			n = n / 2
		}
	}

	for i := 3; i*i <= n; i = i + 2 {
		for n%i == 0 {
			pfs[i] = pfs[i] + 1
			// if pfs[i] == 2 {
			// 	return false
			// }
			n = n / i
			for n%i == 0 {
				n = n / i
			}
		}
	}

	if n > 2 {
		pfs[n] = pfs[n] + 1
	}
	return true
}

// GCD : greatest common divisor (GCD) via Euclidean algorithm
func GCD(a, b int) int {
	for b != 0 {
		t := b
		b = a % b
		a = t
	}
	return a
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 1000000)
	N := getInt()
	a := getInts(N)
	sc := a[0]
	pfs = make(map[int]int)
	PfsMap(a[0])
	for i := 1; i < N; i++ {
		PfsMap(a[i])
		sc = GCD(sc, a[i])
	}
	// out(sc, pfs, a)
	flg := true
	for _, e := range pfs {
		if e != 1 {
			flg = false
			break
		}
	}
	if flg == true {
		out("pairwise coprime")
		return
	}
	if sc == 1 {
		out("setwise coprime")
		return
	}
	out("not coprime")

}