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

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