Coprime

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

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

outputFormat

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

样例

3
6 10 16

not coprime