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: Wrong Answer)

package main

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

func main() {
	sc.Split(bufio.ScanWords)

	n := nextInt()
	ps := primes(1e6 + 10)
	as := make([]int, n)
	gs := make([]int, n+1)
	pm := make(map[int]int)
	for i := 0; i < n; i++ {
		as[i] = nextInt()
		gs[i+1] = gcd(gs[i], as[i])
		pf := primeFactoriation(as[i], ps)
		for p := range pf {
			pm[p]++
		}
	}

	if gs[n] != 1 {
		fmt.Println("not coprime")
		return
	}

	for p, c := range pm {
		if p > 1 && c > 1 {
			fmt.Println("setwise coprime")
			return
		}
	}

	fmt.Println("pairwise coprime")
}

func primes(n int) []int {
	ps := make([]int, n+1)
	for i := 0; i <= n; i++ {
		ps[i] = i
	}
	for i := 2; i*i <= n; i++ {
		if n%i == 0 {
			for j := i + i; j < n; j += i {
				if ps[j] == j {
					ps[j] = i
				}
			}
		}
	}
	return ps
}

func primeFactoriation(n int, ps []int) map[int]int {
	pm := make(map[int]int)
	for n != 1 {
		pm[ps[n]]++
		n /= ps[n]
	}
	return pm
}

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

var sc = bufio.NewScanner(os.Stdin)

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