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C - (K+1)-th Largest Number

Score : $300$ points

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 $K = i-1$.

6
2 7 1 8 2 8

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 $2$.

1
1

1

10
979861204 57882493 979861204 447672230 644706927 710511029 763027379 710511029 447672230 136397527

2
1
2
1
2
1
1
0
0
0