P8658 [Lanqiao Cup 2017 National A] Fill Letters Game

Xiaoming often plays the game LOL and is addicted to it. One time he wanted to challenge Master K, but Master K said: “Let’s first play a game of filling letters into blanks. If you can’t beat me, then don’t play LOL anymore.” Master K draws a row of $n$ cells on paper, and asks Xiaoming and him to take turns filling letters into them. Rules: 1. When it is someone’s turn, they can only fill `L` or `O` into one empty cell. 2. Whoever first makes the letters form the string `LOL` wins. 3. If all cells are filled and `LOL` still cannot be formed, then it is a draw. Xiaoming tried several times and lost every time. He feels ashamed and hopes you can help him solve this puzzle using a computer.

The input format is: The first line contains an integer $n$ ($n

Output $n$ numbers. For each position, if Xiaoming plays first and Master K always uses the strongest moves, output Xiaoming’s best possible result. `1` means Xiaoming can win. `-1` means Xiaoming will definitely lose. `0` means Xiaoming can force a draw.

Time limit: 1 second, 256M. Lanqiao Cup, 2017, the 8th National Finals. Translated by ChatGPT 5