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-----
3
3 4 5

-----Sample Output-----
pairwise coprime

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

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