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Minimum steps

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You are given an array Arr that contains N integers. In one step, you can pick an element from position p and place it before or after some other elements. For example, if you are given an array \(Arr[]\)={\(1,3,2\)}, then you can pick \(3\) and place it after \(2\). Therefore, the updated array is \(Arr[]\)={\(1,2,3\)}.

Your task is to determine the minimum number of steps that is required to sort the data in increasing or decreasing order.

**Input format**

- First line: A single integer
*\(N\)*denoting the size of array \(Arr\) - Second line:
*\(N\)*space-separated integers, where the \(i^{th}\) integer denotes \(Arr[i]\)

**Output format**

Print a single integer value that denotes the minimum number of steps that is required to sort the data in increasing or decreasing order.

**Constraints**

\( 1 \le N \le 5 \times 10^5 \)

\( 1 \le Arr[i] \le 10^9 \)

Explanation

Given **Arr[]={1,3,2}** . For increasing order sorted data Arr will be **{1,2,3}**, steps required is 1. For decreasing order sorted data Arr will be **{3,2,1}**, steps required is 1. So minimum steps are 1.

Time Limit:
1.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

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