{"raw_statement":[{"iden":"problem statement","content":"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 $x$."},{"iden":"constraints","content":"*   $0 \\leq N \\leq 10^4$\n*   $|a_i| \\leq 10^9(0\\leq i\\leq N)$\n*   $a_N \\neq 0$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_N$\n$:$\n$a_0$"},{"iden":"sample input 1","content":"2\n7\n-7\n14"},{"iden":"sample output 1","content":"2\n7\n\n$2$ and $7$ divide, for example, $f(1)=14$ and $f(2)=28$."},{"iden":"sample input 2","content":"3\n1\n4\n1\n5"},{"iden":"sample output 2","content":"There may be no integers that satisfy the condition."},{"iden":"sample input 3","content":"0\n998244353"},{"iden":"sample output 3","content":"998244353"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}