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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分