Given n integers, your task is to determine which algorithm would be the most optimal (Selection, Insertion, or Bubble). You measure the optimality by the number of swaps an algorithm performs during sorting. To do that, you are asked to print the number of swaps that would be performed by each algorithm.

Input

The first line of the input contains a single integer n (1 β€ n β€ ).

The next line contains n space-separated integers ( β€ β€ ).

Output

The program should print the algorithm (Insertion, Selection, Bubble in this order) and the total number of swaps the algorithm would perform to sort the array.

Examples

Input

Output

4
1 4 3 2

Insertion - 3
Selection - 1
Bubble - 3

Tip

Use the implementations from previous exercises to determine the number of swaps