Tired of his stubborn cowlick, Farmer John decides to get a haircut. He has n strands of hair arranged in a line, and strand i is initially ai micrometers long. 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 ai > aj.

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!)

Input

The first line contains n (1 ≤ n ≤ 105). The second line contains a1, a2, ..., an (0 ≤ ai ≤ n).

Output

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++).

Example

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] has five inversions: a1 > a2, a1 > a5, a2 > a5, a3 > a5 and a4 > a5.