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 {
    static int[] factorCnts;
    static boolean checkCoprime = true;

    public static void factorise(int num) {
        if (!checkCoprime)
            return;
        for (int fact = 1; fact * fact <= num; fact++) {
            if (num % fact == 0) {
                int div = num / fact;
                if (fact == div)
                    div = 1;
                if (fact != 1) {
                    if (factorCnts[fact] == 1) {
                        checkCoprime = false;
                        return;
                    }
                    factorCnts[fact]++;
                }
                if (div != 1) {
                    if (factorCnts[div] == 1) {
                        checkCoprime = false;
                        return;
                    }
                    factorCnts[div]++;
                }
            }
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public static void main(String[] args) throws Exception {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(buffer.readLine());
        String[] inp = buffer.readLine().split(" ");
        int[] arr = new int[n];
        arr[0] = Integer.parseInt(inp[0]);
        factorCnts = new int[1000001];
        int gcdRes = arr[0];
        for (int pos = 1; pos < n; pos++) {
            arr[pos] = Integer.parseInt(inp[pos]);
            gcdRes = gcd(gcdRes, arr[pos]);
        }
        for (int pos = 0; pos < n; pos++) {
            factorise(arr[pos]);
        }
        if (checkCoprime) {
            System.out.println("pairwise coprime");
        } else if (gcdRes == 1)
            System.out.println("setwise coprime");
        else
            System.out.println("not coprime");
    }
}
