#P8658. LOL Game Strategy

    ID: 21824 Type: Default 1000ms 256MiB

LOL Game Strategy

LOL Game Strategy

In this game, two players take turns to fill a row of n blank cells with one of the letters L or O. The rules are as follows:

  • On a player's turn, they may choose any empty cell and fill it with either L or O.
  • The game ends immediately when, after a move, there exists a contiguous triple of cells that form the string LOL. Formally, if there exists an index i (1 ≤ i ≤ n-2) such that the cells satisfy $$s_i = L,\; s_{i+1} = O,\; s_{i+2} = L,$$ then the player who just moved wins.
  • If all cells are filled and no such triple appears, the game is a draw.

Observing his previous losses, Xiao Ming wonders if there is a winning strategy. It turns out that if n is at least 3, the first player can always force a win, while if n is less than 3, it is impossible for either player to form the string LOL, resulting in a draw.

Your task is to help Xiao Ming determine the outcome of the game, assuming both players play optimally. Output Win if the first player can force a win, and Draw otherwise.

inputFormat

The input consists of a single integer n (1 ≤ n ≤ 109), representing the number of cells drawn in a row.

outputFormat

Output a single word: Win if the first player can force a win under optimal play (this is the case when n ≥ 3), or Draw if no win is possible (when n < 3).

sample

1
Draw