You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x.

Constraints

* 0 \leq N \leq 10^4
* |a_i| \leq 10^9(0\leq i\leq N)
* a_N \neq 0
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
a_N
:
a_0


Output

Print all prime numbers p that divide f(x) for every integer x, in ascending order.

Examples

Input

2
7
-7
14


Output

2
7


Input

3
1
4
1
5


Output




Input

0
998244353


Output

998244353
import sys
from fractions import gcd
n = int(input())
a = [int(input()) for _ in range(n+1)]
x = 0
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
ps = []

i = 2
while i**2 <= m and i <= n+1:
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
	i += 1
if m != 1 and n != 0:
	ps.append(m)
g = a[0]
for i in range(1, n+1):
	g = gcd(g, abs(a[i]))

ans = []
i = 2
while i**2 <= g:
	if g%i == 0:
		if i >= n+1:
			ans.append(i)
		while g%i == 0:
			g //= i
	i += 1
if g != 1 and g >= n+1:
	ans.append(g)

a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			ans.append(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				ans.append(p)
ans = sorted(list(set(ans)))
if ans:
	print(*ans, sep="\n")