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E - Coprime

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.

3
3 4 5

pairwise coprime

$GCD(3,4)=GCD(3,5)=GCD(4,5)=1$, so they are pairwise coprime.

3
6 10 15

setwise coprime

Since $GCD(6,10)=2$, they are not pairwise coprime. However, since $GCD(6,10,15)=1$, they are setwise coprime.

3
6 10 16

not coprime

$GCD(6,10,16)=2$, so they are neither pairwise coprime nor setwise coprime.