{"raw_statement":[{"iden":"problem statement","content":"Given is an integer $N$. How many permutations $(P_0,P_1,\\cdots,P_{2N-1})$ of $(0,1,\\cdots,2N-1)$ satisfy the following condition?\n\n*   For each $i$ $(0 \\leq i \\leq 2N-1)$, $N^2 \\leq i^2+P_i^2 \\leq (2N)^2$ holds.\n\nSince the number can be enormous, compute it modulo $M$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 250$\n*   $2 \\leq M \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 998244353"},{"iden":"sample output 1","content":"4\n\nFour permutations satisfy the condition:\n\n*   $(2,3,0,1)$\n*   $(2,3,1,0)$\n*   $(3,2,0,1)$\n*   $(3,2,1,0)$"},{"iden":"sample input 2","content":"10 998244353"},{"iden":"sample output 2","content":"53999264"},{"iden":"sample input 3","content":"200 998244353"},{"iden":"sample output 3","content":"112633322"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}