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.