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
import math
n=int(input())
a=list(map(int,input().split()))
table=[0 for i in range(10**6+7)]
flag=0
for i in a:
    table[i]+=1
    
for i in range(2,10**6+1):
    cnt=0
    j=i
    while(j<10**6+1):
        cnt+=table[j]
        j+=i
    if(cnt>1):
        flag=1
        break

if(flag==1):
    tmp=a[0]
    for i in range(1,n):
        tmp=math.gcd(tmp,a[i])
    if(tmp==1):
        flag=2



if(flag==0):
    print('pairwise coprime')
    
if(flag==1):
    print('not coprime')

if(flag==2):
    print('setwise coprime')