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 Julia (1.4.0) (judge verdict: Wrong Answer)

function GCD(a,b)
    return b!=0 ? GCD(b,a%b) : a
end

function main()
    n=parse.(Int,readline())
    A=parse.(Int,split(readline()))
    setwise=false
    pairwise=true
    all_gcd=A[1]
    for i=2:n
        all_gcd=GCD(all_gcd,A[i])
    end
    if all_gcd==1
        setwise=true
    end
    A_max=maximum(A)
    hurui=zeros(Bool,A_max)
    for i=1:n
        hurui[A[i]]=true
    end
    for i=2:floor(Int,sqrt(A_max)+1)
        j=i
        one=false
        while j<=A_max
            if hurui[j]==true && one==false
                one=true
            elseif hurui[j]==true
                pairwise=false
                break
            end
            j+=i
        end
    end
    if pairwise
        println("pairwise coprime")
    elseif setwise
        println("setwise coprime")
    else
        println("not coprime")
    end
end
main()