{"raw_statement":[{"iden":"problem statement","content":"Let $f(n)$ be the number of triples of integers $(x,y,z)$ that satisfy both of the following conditions:\n\n*   $1 \\leq x,y,z$\n*   $x^2 + y^2 + z^2 + xy + yz + zx = n$\n\nGiven an integer $N$, find each of $f(1),f(2),f(3),\\ldots,f(N)$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 10^4$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"20"},{"iden":"sample output 1","content":"0\n0\n0\n0\n0\n1\n0\n0\n0\n0\n3\n0\n0\n0\n0\n0\n3\n3\n0\n0\n\n*   For $n=6$, only $(1,1,1)$ satisfies both of the conditions. Thus, $f(6) = 1$.\n*   For $n=11$, three triples, $(1,1,2)$, $(1,2,1)$, and $(2,1,1)$, satisfy both of the conditions. Thus, $f(6) = 3$.\n*   For $n=17$, three triples, $(1,2,2)$, $(2,1,2)$, and $(2,2,1)$, satisfy both of the conditions. Thus, $f(17) = 3$.\n*   For $n=18$, three triples, $(1,1,3)$, $(1,3,1)$, and $(3,1,1)$, satisfy both of the conditions. Thus, $f(18) = 3$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}