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
def gcd(a, b):
	while b:
		a, b = b, a % b
	return a

def prime_decomposition(n):
  i = 2
  d = {}
  while i * i <= n:
    while n % i == 0:
      n //= i
      if i not in d:
          d[i] = 0
      d[i] += 1
    i += 1
  if n > 1:
    if n not in d:
        d[n] = 1
  return d

def eratosthenes(n):
    if n < 2:
        return []
    prime = []
    limit = n**0.5
    numbers = [i for i in range(2,n+1)]
    while True:
        p = numbers[0]
        if limit <= p:
            return prime + numbers
        prime.append(p)
        numbers = [i for i in numbers if i%p != 0]
    return prime

def ok(p):
    if A[0]%p != 0:
        return False
    B = [A[i]%p for i in range(1,N+1)]
    mod = [0]*(p-1)
    for i in range(N):
        mod[i%(p-1)] += B[i]
        mod[i%(p-1)] %= p
    return sum(mod)==0

N = int(input())
A = [int(input()) for i in range(N+1)][::-1]
g = abs(A[0])
for a in A:
     g = gcd(g,abs(a))
d = prime_decomposition(g)
ans = [p for p in d]

prime = eratosthenes(N+1)

for p in prime:
    if ok(p):
        ans.append(p)

ans = list(set(ans))
ans.sort()

for p in ans:
    print(p)