Problem:
Score : 500 points

Problem Statement

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 1

3
3 4 5

Sample Output 1

pairwise coprime

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

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.

Solution in OCaml (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d" (fun n ->
    let div = Array.make 1000000 0 in
    let rec gcd a b = if b = 0 then a else gcd b (a mod b) in
    let rec loop i g =
        if i = n then g else
            let g = Scanf.scanf " %d" (fun a ->
                let g = gcd a g in
                let rec loop r i =
                    if r = 1 then () else
                    if i * i > r then div.(r) <- div.(r) + 1 else
                        if r mod i <> 0 then loop r (i + 1) else
                            let () = div.(i) <- div.(i) + 1 in
                            let rec loop2 r =
                                if r mod i = 0 then loop2 (r / i) 
                                    else loop r (i + 1)
                            in
                            loop2 r
                in
                loop a 2;
                g
            )
            in
            loop (i + 1) g
    in
    let g = loop 0 0 in
    print_endline @@
        if g <> 1 then "not coprime" else
            if Array.fold_left max 0 div <= 1 then "pairwise coprime" else "setwise coprime"
)