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.

Examples

Input

3
3 4 5

Output

pairwise coprime

Input

3
6 10 15

Output

setwise coprime

Input

3
6 10 16

Output

not coprime

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