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.