In a secret base №4652 during a process of up-to-date intelligent electric kettles manufacture a special nanosoldering device is used. The nanosoldering device connects contacts on nanochips directly. The contacts on the nanochips are numbered and their coordinates are set.
Task. Calculate the order of the contacts connection if the nanosoldering devise route starts and finishes on the contact number 1 and the connective lines should not cross. At each soldering step a contact with biggest number has higher priority.
Streams. Input stream contains number of contacts K (integer) and couples of coordinates for each separate contacts xi and yi (integers), where i = 1, 2, ... К. Output stream contains K+1 integers.
ExampleInput stream:4 0 0 1 0 0 1 1 1Output stream:1 3 4 2 1