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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int gcd(int a, int b) {
	while (b > 0) {
		int r = a % b;
		a = b;
		b = r;
	}
	return a;
}

#define MAX 1123456

int N;
int A[MAX];

int era[MAX];
char exists[MAX];

int main(void) {
	int i, j;
	int good = 1;
	if (scanf("%d", &N) != 1) return 1;
	for (i = 0; i < N; i++) {
		if (scanf("%d", &A[i]) != 1) return 1;
	}
	for (i = 2; i < MAX; i++) {
		if (era[i] == 0) {
			era[i] = i;
			for (j = i + i; j < MAX; j += i) {
				if (era[j] == 0) era[j] = i;
			}
		}
	}
	for (i = 0; i < N; i++) {
		if (A[i] > 1) {
			if (exists[A[i]] == 2) {
				puts("not coprime");
				return 0;
			}
			exists[A[i]] = 2;
			j = A[i] / era[A[i]];
			while (j > 1) {
				if (exists[j] > 0) good = 0; else exists[j] = 1;
				j /= era[A[i]];
			}
		}
	}
	if (good) {
		puts("pairwise coprime");
	} else {
		int g = A[0];
		for (i = 1; i < N; i++) g = gcd(g, A[i]);
		printf("%s coprime\n", g == 1 ? "setwise" : "not");
	}
	return 0;
}