Problem Statement

You are given a sequence ~A = (A_1, A_2, \ldots, A_N)~ of length ~N~ . For each ~K = 0, 1, 2, \ldots, N-1~ , solve the following problem.

Find the number of integers ~i~ between ~1~ and ~N~ (inclusive) such that:

• ~A~ contains exactly ~K~ distinct integers greater than ~A_i~ .

Constraints

• ~1 \leq N \leq 2 \times 10^5~
• ~1 \leq A_i \leq 10^9~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~

~A_1~ ~A_2~ ~\ldots~ ~A_N~

Output

Print ~N~ lines. For ~i = 1, 2, \ldots, N~ , the ~i~ -th line should contain the answer for ~K = i-1~ .

Sample Input 1

6
2 7 1 8 2 8

Sample Output 1

2
1
2
1
0
0

For example, we will find the answer for ~K=2~ .

• Regarding ~A_1 = 2~ , ~A~ contains ~2~ distinct integers greater than ~A_1~ : ~7~ and ~8~ .
• Regarding ~A_2 = 7~ , ~A~ contains ~1~ distinct integer greater than ~A_2~ : ~8~ .
• Regarding ~A_3 = 1~ , ~A~ contains ~3~ distinct integers greater than ~A_3~ : ~2, 7~ , and ~8~ .
• Regarding ~A_4 = 8~ , ~A~ contains ~0~ distinct integers greater than ~A_4~ (there is no such integer).
• Regarding ~A_5 = 2~ , ~A~ contains ~2~ distinct integers greater than ~A_5~ : ~7~ and ~8~ .
• Regarding ~A_6 = 8~ , ~A~ contains ~0~ distinct integers greater than ~A_6~ (there is no such integer).

Thus, there are two ~i~ 's, ~i = 1~ and ~i = 5~ , such that ~A~ contains exactly ~K = 2~ distinct integers greater than ~A_i~ . Therefore, the answer for ~K = 2~ is ~2~ .

Sample Input 2

1
1

Sample Output 2

1

Sample Input 3

10
979861204 57882493 979861204 447672230 644706927 710511029 763027379 710511029 447672230 136397527

Sample Output 3

2
1
2
1
2
1
1
0
0
0