A sequence of integers is called a wonderful sequence if all the integers in it are positive and it is a strictly increasing sequence.

Given a sequence of integers, you have to make it a wonderful sequence. For that you can change any element you want, but you should make as less changes as possible in order to make it a wonderful sequence.

Input

The first line of input is an integer T(T <= 5), the number of test cases. Each test case contains 2 lines.

The first line of the test case contains an integer (0 < N <= 100000), i.e. the number of elements in the original sequence.

The second line contains N positive integers, no larger than 2000000000, which forms the original sequence.

Output

For each test case output the minimal number of elements you must change in the original sequence to make it a wonderful sequence.