Sort the numbers

Given n integers, you are asked to sort them in increasing order. During each operation, you are allowed to pick one element and move it to the very beginning of the array. What would be the minimum number of operations to sort the array?

Input

The first line of the input contains a single integer n (1 ≀ n ≀ ).
The next line contains n space-separated integers (1 ≀ ≀ ) array elements.

Output

The program should print the minimum number of operations required to sort the array.

Examples

Input
Output
6 11 13 15 12 14 16
4
10 1 3 2 4 2 4 4 5 9 10
3

Explanation of the 1st Example

  1. Move 14 to the beginning
  1. Move 13 to the beginning
  1. Move 12 to the beginning
  1. Move 11 to the beginning

Explanation of the 2nd Example

  1. Move 2 to the beginning
  1. Move the other 2 to the beginning
  1. Move 1 to the beginning
Β 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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