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 -*-
import sys
from collections import defaultdict
from fractions import gcd
N=int(sys.stdin.readline().strip())
A=map(int, sys.stdin.readline().split())

def factorization(n):
    arr=set()
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.add(i)

    if temp!=1:
        arr.add(temp)

    if arr==[]:
        arr.add(n)

    return arr

pairwise_coprime=True

SOINSU=defaultdict(lambda: 0)

setwise_coprime=None
for i,a in enumerate(A):
    #全ての数が互いに素か　pairwise coprime判定
    if pairwise_coprime==False:
        pass
    else:
        f=factorization(a)
        for x in f:
            if SOINSU[x]==1:
                pairwise_coprime=False
                break
            SOINSU[x]=1
    #GCDの累積を取る　setwise coprime判定
    if i==0:
        setwise_coprime=a
    else:
        setwise_coprime=gcd(setwise_coprime,a)

if pairwise_coprime==True:
    print "pairwise coprime"
elif setwise_coprime==1:
    print "setwise coprime"
else:
    print "not coprime"