Minimum insertions to sort an array

Given an array of integer numbers, we need to sort this array in a minimum number of steps where in one step we can insert any array element from its position to any other position.

 

Input:

The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains an integer N denoting the size of array A.

The second line of each test case contains N space separated integers denoting elements of the array A[ ].
Output:

Output the minimum steps needed to sort the array. Print the answer for each test case in a new line.
Constraints:

1<= T <=100

1<= N <=1000

1<= A[ ] <=1000
Example:

Input:

1

7

2 3 5 1 4 7 6

Output:

3

**For More Examples Use Expected Output**

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rakesh

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