Root NIM#3505
The game root NIM uses the next rules. There is a heap of stones before two players. They take out the stones in turns. If the heap contains stones, the player can take out of it any number of stones from to \lfloor\sqrt{k}\rfloor inclusively. For example from the heap of stones its possible to take , or stones. The player who cannot make a move loses.
By the given value of determine whether the first player can win during optimal play of both players.
One number (1 \le n \le 10^{12}) - the number of stones in the heap.
Print WIN if the first player wins and LOSE if the first player can't win.
Example 1
Example 2