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: Runtime Error)

N = int(input())
A = list(map(int, input().split()))
dictA = dict()
for a in A:
  if a in dictA.keys():
    dictA[a] += 1
  else:
    dictA[a] = 1

def get_prime(p):
  result = []
  if p==1:
    return result
  else:
    integers = [1 for _ in range(p+1)]
    integers[0] = 0
    integers[1] = 0
    for i in range(p+1):
      if integers[i] == 1:
        result.append(i)
        for j in range(i,p+1,i):
          integers[j] = 0
    return result

def count_coprime(p):
  count = 0
  for a,v in dictA.items():
    if a%p == 0:
      count += v
  return count

maxA = max(A)
answer = 'pairwise coprime'
if maxA > 1:
  if max(dictA.values()) == N:
    answer = 'not coprime'
    break
  if max(dictA.values()) >= 2:
    answer = 'setwise coprime'
  for p in get_prime(1001):
    count = count_coprime(p)
    if count == N:
      answer = 'not coprime'
      break
    elif count >= 2:
      answer = 'setwise coprime'

print(answer)