Score : $500$ points
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 is given from Standard Input in the following format:
$N$ $A_1$ $\ldots$ $A_N$
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.