Elaine is a farmer. Today she got a farmland from her grand-grand-grand-...-grand-father.
In fact, that's a forest with a number of trees. She decide to cut down many trees and leave some. Then she will encircle her farmland with the left trees.
To make her farmland as bigger as possible, which trees should she leave?

This problem has several cases. The first line of each case is an integer N (2 < N <= 100000).
Then follow N lines. The ith line is the coordinate of ith tree. (Count i from 0).
You should consider that there's no possible that all trees are in a line.

For each case, you should output the number of each left tree. From small to big.