A dance with 2018 couples takes place in Havana. For the dance, 2018 distinct points labeled 0,1,…,2017 are marked in a circumference and each couple is placed on a different point. For i≥1, let si=i (mod 2018) and ri=2i (mod 2018). The dance begins at minute 0. On the i-th minute, the couple at point si (if there's any) moves to point ri, the couple on point ri (if there's any) drops out, and the dance continues with the remaining couples. The dance ends after 20182 minutes. Determine how many couples remain at the end. Note: If ri=si, the couple on si stays there and does not drop out. combinatoricsCentroamerican