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 Python (3.8.2) (judge verdict: Wrong Answer)

from math import gcd

def make_prime(n):
    array = set()
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                temp = temp // i
            array.add(i)

    if temp != 1:
        array.add(temp)

    if not array:
        array.add(n)

    return array


N = int(input())
A = list([int(x) for x in input().split()])

result = set()
before = -1
is_pairwise = True
for i in A:
    i_r = make_prime(i)
    if len(result & i_r) > 0:
        is_pairwise = False
    else:
        result |= i_r

    if before == -1:
        before = i
    else:
        before = gcd(i, before)

if is_pairwise:
    print('pairwise coprime')
    exit()

if before == 1:
    print('setwise coprime')
    exit()

print('not coprime')