Score : 1600 points
There are N integers written on a blackboard. The i-th integer is A_i.
Takahashi and Aoki will arrange these integers in a row, as follows:
We will assume that Takahashi acts optimally so that the eventual sequence will be lexicographically as small as possible, and we will also assume that Aoki acts optimally so that the eventual sequence will be lexicographically as large as possible. Find the eventual sequence that will be produced.
The input is given from Standard Input in the following format:
N A_1 A_2 … A_N
Print the eventual sequence that will be produced, in a line.
5 1 2 3 4 5
5 3 2 4 1
If Takahashi arranges the given integers in the order (1,2,3,4,5), they will become (5,3,2,4,1) after Aoki optimally manipulates them.
4 2 3 4 6
2 4 6 3