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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

from math import gcd

"""
pairwise coprimeであるための条件は、全てのAに関して素因数に重複がないことである。
したがって、各Aに関して素因数分解を行う⇒各数の素因数の種類数をカウントし総和する。⇒全体の素因数の種類数をカウントし、先ほどの総和と比較する。
"""
N = int(input())
A = list(map(int,input().split()))
primes = []
def primeFinder(n):
    memo = [1]*(n+1)
    memo[0] = 0
    memo[1] = 0
    for i in range(2,n+1):
        if memo[i] == 1:
            primes.append(i)
            for j in range(i*2,n+1,i):
                memo[j] = 0
primeFinder(1000000)

primeMemo = set()
cnt = 0
for i in range(N):
    a = A[i]
    for p in primes:
        if p*p > a:
            break
        if a%p == 0:
            cnt += 1
            primeMemo.add(p)
        while a%p==0:
            a //= p
    if a != 1:
        cnt += 1
        primeMemo.add(a)

if cnt == len(primes):
    print('pairwise coprime')
    exit()
g = A[0]
for i in range(1,N):
    g = gcd(g,A[i])
if g == 1:
    print('setwise coprime')
else:
    print('not coprime')