reverse order 1

Time Limit : 1 Second

Memory Limit : 128 MB

Submission: 691

Solved: 144

Description


Here is a sequence a1..n, which is a disordered sequence from 1 to N. If i < j and ai > aj, then <i, j> is called a pair of inversion. And b1..n-1 is defined as follows, bk is the number of the total inversion pairs in array a, when i<=k<j. Now the array b is required while the array a is known.


Input


Several cases end with the end of the file;



And each of the cases includes two lines, a integer n(2<=n<=10^5)in the first line, and the second line followed with n integer, which is in the presentation of array a;


Output


Output the answer of each case in a line, namely the array b, and a space is required between the adjacent integers.


sample input
5
3 1 4 2 5
sample output
2 1 2 0
hint
source
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