Score : $800$ points

Problem Statement

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.

2
7
-7
14

2
7

$2$ and $7$ divide, for example, $f(1)=14$ and $f(2)=28$.

3
1
4
1
5

There may be no integers that satisfy the condition.

0
998244353

998244353