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, sqrt
from functools import reduce

n, *A = map(int, open(0).read().split())
def f(A):
    sup = max(A)+1
    table = [{i} for i in range(sup)]
    table[0] = set()
    table[1] = set()
    for i in range(2, int(sqrt(sup))+1):
        if len(table[i]) == 1:
            for j in range(i**2, sup, i):
                table[j].add(i)
    D = table[A[0]]
    for a in A[1:]:
        for b in table[a]:
            if b not in D:
                D.add(b)
            else:
                return False
    return True

if reduce(gcd, A) == 1:
    if f(A):
        print('pairwise coprime')
    else:
        print('setwise coprime')
else:
    print('not coprime')