Indian National Olympiad in Informatics

Online Programming Contest, 10-11 September 2005


Advanced Division

Problem 1: Book Sorting, (K Narayan Kumar, CMI)

Indraneel has to sort the books in his library. His library has one long shelf. His books are numbered 1 through N and he wants to rearrange the books so that they appear in the sequece 1,2, ..., N.

He intends to do this by a sequence of moves. In each move he can pick up any book from the shelf and insert it at a different place in the shelf. Suppose Indraneel has 5 books and they are initially arranged in the order

2 1 4 5 3

Indraneel will rearrange this in ascending order by first moving book 1 to the beginning of the shelf to get

1 2 4 5 3

Then, moving book 3 to position 3, he gets

1 2 3 4 5

Your task is to write a program to help Indraneel determine the minimum number of moves that are necessary to sort his book shelf.

Input format

The first line of the input will contain a single integer N indicating the number of books in Indraneel's library. This is followed by a line containing a permutation of 1, 2, ..., N indicating the intial state of Indraneel's book-shelf.

Output format

A single integer indicating the minimum number of moves necessary to sort Indraneel's book-shelf.

Test Data:

You may assume that 1 ≤ N ≤ 200000. You may also assume that in 50% of the inputs, 1 ≤ N ≤ 5000.


Here is the sample input and output corresponding to the example discussed above.

Sample Input

2 1 4 5 3 

Sample Output


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