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 sys
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))  #空白あり


N = I()
A = LI()


from math import gcd

g = 0  # Aiたちの最大公約数
for i in range(N):
    g = gcd(g,A[i])

if g != 1:
    print('not coprime')
    exit()


B = [0]*(10**6+1)
for i in range(N):
    B[A[i]] += 1

for d in range(2,5*10**5+1):
    a = sum(B[i] for i in range(d,10**6+1,d))
    if a >= 2:
        print('setwise coprime')
        break
else:
    print('pairwise coprime')

# 計算量 O(A*logA)
# A = max(Ai)
