{"raw_statement":[{"iden":"problem statement","content":"On a 2D coordinate plane, there is a piece placed at $(0, 0)$.  \nYou will perform the following operation $N$ times:\n\n*   Choose an integer $i$ such that $0 \\leq i \\leq 11$.  \n    If the current position of the piece is $(x, y)$, move it to $(x + \\cos(30i)^\\circ, y + \\sin(30i)^\\circ)$.\n\nCount the number of operation sequences that result in the piece being back at $(H, W)$ after $N$ operations, and output the result modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2.5 \\times 10^5$\n*   $-N \\leq H \\leq N$\n*   $-N \\leq W \\leq N$\n*   $N, H, W$ are integers"},{"iden":"partial score","content":"This problem has partial scoring:\n\n*   If you solve all datasets with $(H, W) = (0, 0)$, you will earn $5$ points."},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$N$ $H$ $W$"},{"iden":"sample input 1","content":"2 0 0"},{"iden":"sample output 1","content":"12\n\nFor every integer $n$ such that $0 \\leq n \\leq 11$, if the first operation chooses $i = n$ and the second operation chooses $i = (n+6) \\bmod 12$, the condition is satisfied. Thus, there are $12$ valid sequences."},{"iden":"sample input 2","content":"123456 0 0"},{"iden":"sample output 2","content":"352845935"},{"iden":"sample input 3","content":"50 -12 34"},{"iden":"sample output 3","content":"391874286"},{"iden":"sample input 4","content":"234567 89012 -34567"},{"iden":"sample output 4","content":"523418763"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}