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()))

MAX = max(A)

# remap
AR = [0] * (MAX+1)
V = [False] * (MAX+1)
for i in range(N): AR[A[i]] += 1
pairwise, setwise = True, True

# sieve
for i in range(2, MAX+1):
    if V[i]: continue
    cnt, j = 0, i
    while j < MAX+1:
        cnt += AR[j]
        V[j] = True
        j += i
    if cnt > 1: pairwise = False
    if cnt == len(A): setwise = False

if pairwise:
    print('pairwise coprime')
elif setwise:
    print('setwise coprime')
else:
    print('not coprime')