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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

	public static String Y = "Yes";
	public static String N = "No";
	public static long MOD = (long) (Math.pow(10, 9) + 7);
	public static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {

		int n = ni();
		int[] a = new int[n];
		a[0] = ni();
		int gcd = a[0];
		for (int i = 1; i < n; i++) {
			a[i] = ni();
			gcd = gcd(gcd, a[i]);
		}
		if (gcd != 1) {
			out("not coprime");
			return;
		}

		int[] d = kousokusoinnsuubunkaihairetsu(1000009);

		long count = 0;
		Set<Integer> soinnsuu = new HashSet<>();
		Set<Integer> soinnsuutmp = null;

		for (int i = 0; i < n; i++) {
			int aa = a[i];
			soinnsuutmp = new HashSet<>();
			//debug(aa);
			for (;;) {
				soinnsuutmp.add(aa);
				if (aa == d[aa]) {
					break;
				} else {
					soinnsuutmp.add(d[aa]);
					aa /= d[aa];
					soinnsuutmp.add(aa);
				}
			}
			count += soinnsuutmp.size();
			soinnsuu.addAll(soinnsuutmp);
			//debug();
		}

		if ((int) count != soinnsuu.size()) {
			out("setwise coprime");
			return;
		}
		out("pairwise coprime");
	}

	/*
	 * 以下メソッド集
	 */

	public static int[] kousokusoinnsuubunkaihairetsu(int a) {
		int[] d = new int[a];
		for (int i = 0; i < a; i++) {
			d[i] = i;
		}
		for (int i = 2; i * i < a; i++) {
			for (int j = i * i; j < a; j += i) {
				if (d[j] == j)
					d[j] = i;
			}

		}

		return d;
	}

	public static void permutation(String q, String ans) {
		// Base Case
		if (q.length() <= 1) {
			System.out.println(ans + q);
		}
		// General Case
		else {
			for (int i = 0; i < q.length(); i++) {
				permutation(q.substring(0, i) + q.substring(i + 1),
						ans + q.charAt(i));
			}
		}
	}

	static char[][] same(char[][] c, int h, int w) {

		char[][] a = new char[h][w];
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				a[i][j] = c[i][j];
			}
		}
		return a;

	}

	static int countkuro(char[][] c) {

		int count = 0;
		for (char[] cc : c) {
			for (char ccc : cc) {
				if ('#' == ccc) {
					count++;
				}
			}
		}
		return count;
	}

	static void debug() {

		out("---");
	}

	static void debug(Object a) {

		out("-------");
		out(a);
		out("-------");
	}

	static int ketasuu(int n) {

		String str = "" + n;
		return str.length();
	}

	static int account(String str) {

		String target = "AC";
		int count = 0;
		int len = str.length();
		for (int i = 0; i < len - 1; i++) {
			if (target.equals(str.substring(i, i + target.length()))) {
				count++;
			}
		}
		return count;
	}

	static int ni() {

		return sc.nextInt();
	}

	static long nl() {

		return sc.nextLong();
	}

	static double nd() {

		return sc.nextDouble();
	}

	static String n() {

		return sc.next();
	}

	static char[] nc() {

		return sc.next().toCharArray();
	}

	static int kaijo(int n) {

		if (n == 0 || n == 1) {
			return 1;
		} else {
			return n * kaijo(n - 1);
		}
	}

	static int fib(int n) {

		return (n == 1 || n == 0) ? n : fib(n - 2) + fib(n - 1);
	}

	static long lcm(long m, long n) {

		return m * n / gcd(m, n);
	}

	static int lcm(int m, int n) {

		return m * n / gcd(m, n);
	}

	static long gcd(long a, long b) {

		return (b == 0) ? a : gcd(b, a % b);
	}

	static int gcd(int a, int b) {

		return (b == 0) ? a : gcd(b, a % b);
	}

	static void out(Object obj) {
		System.out.println(obj);
	}

	static void outn(Object obj) {
		System.out.print(obj);
	}

	static double max(double d, double e) {

		return Math.max(d, e);
	}

	static long max(long a, long b) {

		return Math.max(a, b);
	}

	static long min(long d, long e) {

		return Math.min(d, e);
	}

	static int min(int a, int b) {

		return Math.min(a, b);
	}
}

class XY {

	int h;
	int w;
	int d;

	XY(int h, int w, int d) {
		this.h = h;
		this.w = w;
		this.d = d;
	}
}