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
n = int(input())
a = list(map(int,input().split()))
import sys

num = 10**6
li = [0]*num
for k in a:
    li[k-1] += 1

i=2
while i<=num:
    if sum([li[k*i-1] for k in range(1,num//i+1)])>1:
        break
    i+=1
else:
    print("pairwise coprime")
    sys.exit()

import math
import functools
g = functools.reduce(math.gcd,a)
if g==1:
    print("setwise coprime")
    sys.exit()

print("not coprime")
