PROGRAMMING:Little Gyro and Numbers
Little Gyro has just found a number sequence $$a_ 1,a_ 2,...,a_ n$$ which length is $$n$$ in his right pocket, while his left pocket is totally empty. As Little Gyro is bored, he decides to play with these numbers.
Then, Little Gyro is prepared to play with the number sequence with $$n$$ operations by doing the following steps:
1. In the $$i$$-th turn, Little Gyro will take out a number $$a_ i$$ from his right pocket with its initial permutation, as well as put it into his left pocket.
2. Then, Little Gyro let number $$p = a_ i$$.
3. After that, Little Gyro take out a number $$a_ j$$ from all the remained numbers in his right pocket one by one, set down the number and let number $$q = a_ j$$, and then put the number $$a_ j$$ back to his right pocket immediately.
4. Finally, for each number pair $$$$, Little Gyro will calculate $$p^q$$ and $$q^p$$, and count how many pairs of numbers satisfied $$p^q > q^p$$. After counting all the number pairs of the $$i$$-th turn, Little Gyro put the number $$a_ i$$ back to his right pocket with its initial position.
Now given an integer sequence, after these operations, Little Gyro wants to know the number of all the satisfied number pairs of each turn and ask you for help, please help him to count.
### Input Specification:
There are multiple test cases. The first line of the input contains an integer $$T$$, indicating the number of test cases. For each test case:
The first line contains an integer $$n$$ (2 ≤ $$n$$ ≤ $$10^5$$), indicating the length of the sequence.
The second line contains $$ n$$ integers $$a_ 1,a_ 2,...,a_ n$$ (1 ≤ $$a_ i$$ ≤ $$10^9$$), indicating the given sequence.
It's guaranteed that the sum of $$ n$$ of all test cases will not exceed $$10^6$$.
### Output Specification:
For each test case, you should firstly print `Case X:` in the first line, indicating the case number.
And then output $$n$$ lines, the $$i$$-th line contains an integer indicating the number of all the satisfied number pairs of number $$a_ i$$ in the $$i$$-th turn.
### Sample Input:
```in
two
three
1 2 5
four
4 5 6 7
```
### Sample Output:
```out
Case 1:
0
two
one
Case 2:
three
two
one
0
```
answer：If there is no answer, please comment
Then, Little Gyro is prepared to play with the number sequence with $$n$$ operations by doing the following steps:
1. In the $$i$$-th turn, Little Gyro will take out a number $$a_ i$$ from his right pocket with its initial permutation, as well as put it into his left pocket.
2. Then, Little Gyro let number $$p = a_ i$$.
3. After that, Little Gyro take out a number $$a_ j$$ from all the remained numbers in his right pocket one by one, set down the number and let number $$q = a_ j$$, and then put the number $$a_ j$$ back to his right pocket immediately.
4. Finally, for each number pair $$
Now given an integer sequence, after these operations, Little Gyro wants to know the number of all the satisfied number pairs of each turn and ask you for help, please help him to count.
### Input Specification:
There are multiple test cases. The first line of the input contains an integer $$T$$, indicating the number of test cases. For each test case:
The first line contains an integer $$n$$ (2 ≤ $$n$$ ≤ $$10^5$$), indicating the length of the sequence.
The second line contains $$ n$$ integers $$a_ 1,a_ 2,...,a_ n$$ (1 ≤ $$a_ i$$ ≤ $$10^9$$), indicating the given sequence.
It's guaranteed that the sum of $$ n$$ of all test cases will not exceed $$10^6$$.
### Output Specification:
For each test case, you should firstly print `Case X:` in the first line, indicating the case number.
And then output $$n$$ lines, the $$i$$-th line contains an integer indicating the number of all the satisfied number pairs of number $$a_ i$$ in the $$i$$-th turn.
### Sample Input:
```in
two
three
1 2 5
four
4 5 6 7
```
### Sample Output:
```out
Case 1:
0
two
one
Case 2:
three
two
one
0
```
answer：If there is no answer, please comment