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`.

Examples

Input

3
3 4 5


Output

pairwise coprime


Input

3
6 10 15


Output

setwise coprime


Input

3
6 10 16


Output

not coprime
#include <cstdio>
int n,a,d,t[1000003],maxa=-(1<<30);
int gcd(int x,int y){
    if(!y) return x;
    return gcd(y,x%y);
}
void fj(int x){
    for(int i=2;i*i<=x;){
        if(!(x%i)){
            ++t[i];
            while(!(x%i)) x/=i;
        }
        else ++i;
    }
    if(x>1) ++t[x];
}
int main(){
    scanf("%d%d",&n,&a),d=a;
    for(int i=2;i<=n;i++){
        scanf("%d",&a);
        if(maxa<a) maxa=a;
        d=gcd(d,a);
        fj(a);
    }
    if(d==1){
        for(int i=2;i<=maxa;i++) if(t[i]>1) return puts("setwise coprime"),0;
        return puts("pairwise coprime"),0;
    }
    else return puts("not coprime"),0;
    return 0;
}