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
import java.io.*;
import java.util.*;

public class Main {
    public static final long mod = (long)1e9+7;
    public static final long INF = Long.MAX_VALUE/2;
    public static final int inf = Integer.MAX_VALUE/2;

    static void solve(InputReader in, PrintWriter out){
        int n = in.ni();
        long[] a = in.nl(n);
        long gcd = a[0];
        for (int i = 0; i < n; i++) gcd = gcd(gcd, a[i]);
        if(gcd != 1){
            out.println("not coprime");
        }else{
            TreeMap<Long, Integer> tm = new TreeMap<Long, Integer>();
            boolean[] used = new boolean[1000001];
            boolean flag = true;
            OUT:for (int i = 0; i < n; i++) {
                tm = PrimeFactorization(a[i]);
                for(long key: tm.keySet()){
                    if(used[(int)key]){
                        flag = false;
                        break OUT;
                    }else{
                        used[(int)key] = true;
                    }
                }
            }
            out.println(flag?"pairwise coprime":"setwise coprime");
        }
    }
    public static long gcd(long a, long b){
        long c;
        if(a < b){
            c = a;
            a = b;
            b = c;
        }
        while(b > 0){
            c = a;
            a = b;
            b = c%b;
        }
        return a;
    }
    public static TreeMap<Long, Integer> PrimeFactorization(long n){
            TreeMap<Long, Integer> map = new TreeMap<>();
            long N = n;
            for (long i = 2; i*i <= N; i++) {
                while(n%i==0){
                    map.put(i, map.containsKey(i)?map.get(i)+1:1);
                    n /= i;
                }
            }
            if(n!=1) map.put(n, 1);
            return map;
    }

    public static void main(String[] args){
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        solve(in, out);
        out.close();
    }
    public static class InputReader{
        private BufferedReader br;
        private StringTokenizer st;
        public InputReader(InputStream is){
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }
        public String ns(){
            if(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (Exception e){
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
        public int ni(){
            return Integer.parseInt(ns());
        }
        public long nl(){
            return Long.parseLong(ns());
        }
        public double nd(){
            return Double.parseDouble(ns());
        }
        public char nc(){
            return ns().toCharArray()[0];
        }
        public int[] ni(int n){
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }
        public long[] nl(int n){
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }
        public double[] nd(int n){
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }
    }
}