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.