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
# coding: utf-8
# Your code here!
import sys
readline = sys.stdin.readline
read = sys.stdin.read

n,*a = map(int,read().split())

M = 10**6
r = [0]*(M+1)
for i in a:
    r[i] += 1


isp = True
for x in range(2,M+1):
    c = sum(r[x::x])
    if c == n:
        print("not coprime")
        exit()
    if c >= 2:
        isp = False
else:
    if isp:
        print("pairwise coprime")
    else:
        print("setwise coprime")







