Tired of his stubborn cowlick, Farmer John decides to get a haircut. He has N (1≤N≤10⁵) strands of hair arranged in a line, and strand i is initially A_i micrometers long (0≤A_i≤N). Ideally, he wants his hair to be monotonically increasing in length, so he defines the "badness" of his hair as the number of inversions: pairs (i,j) such that i<j and A_i>A_j.
For each of j=0,1,…,N−1, FJ would like to know the badness of his hair if all strands with length greater than j are decreased to length exactly j.

(Fun fact: the average human head does indeed have about 105 hairs!)

The first line contains N.
The second line contains A1,A2,…,AN.

For each of j=0,1,…,N−1, output the badness of FJ's hair on a new line.
Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

5
5 2 3 3 0

0
4
4
5
7

The fourth line of output describes the number of inversions when FJ's hairs are decreased to length 3. Then A=[3,2,3,3,0]A=[3,2,3,3,0] has five inversions: A1>A2,A1>A5,A2>A5,A3>A5,A1>A2,A1>A5,A2>A5,A3>A5, and A4>A5

Test case 2 satisfies N≤100.
Test cases 3-5 satisfy N≤5000.
Test cases 6-13 satisfy no additional constraints.