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: Time Limit Exceeded)

let as_num_list s =
  let splitted = String.split_on_char ' ' s in
  List.map int_of_string splitted

let rec gcd a b =
  if b = 0
  then a
  else gcd b (a mod b)

let main () =
  let n = Scanf.sscanf (read_line ()) "%d" (fun x -> x) in
  let as_str = read_line () in
  let a_list = as_num_list as_str in
  let sum = ref 0 in
  let isPairwise = ref true in
  (
    for i = 0 to n - 2 do
      for j = i + 1 to n - 1 do
        if gcd (List.nth a_list i) (List.nth a_list j) <> 1
        then isPairwise := false
      done
    done;
    if !isPairwise
    then Printf.printf "pairwise coprime"
    else
      if List.fold_left gcd (List.hd (List.sort compare a_list)) a_list = 1
      then Printf.printf "setwise coprime"
      else Printf.printf "not coprime";
    print_newline ()
  )

let _ = main ()