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.

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.

Constraints

• $2 \leq N \leq 10^6$
• $1 \leq A_i\leq 10^6$

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.

见题面 Input 部分

见题面 Output 部分