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D - Strange Balls

Score : $400$ points

Problem Statement

Takahashi has $N$ balls. Each ball has an integer not less than $2$ written on it. He will insert them in a cylinder one by one. The integer written on the $i$-th ball is $a_i$.

The balls are made of special material. When $k$ balls with $k$ $(k \geq 2)$ written on them line up in a row, all these $k$ balls will disappear.

For each $i$ $(1 \leq i \leq N)$, find the number of balls after inserting the $i$-th ball.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $2 \leq a_i \leq 2 \times 10^5 \, (1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $\ldots$ $a_N$

Output

Print $N$ lines. The $i$-th line $(1 \leq i \leq N)$ should contain the number of balls after inserting the $i$-th ball.

5
3 2 3 2 2

1
2
3
4
3

The content of the cylinder changes as follows.

• After inserting the $1$-st ball, the cylinder contains the ball with $3$.
• After inserting the $2$-nd ball, the cylinder contains $3, 2$ from bottom to top.
• After inserting the $3$-rd ball, the cylinder contains $3, 2, 3$ from bottom to top.
• After inserting the $4$-th ball, the cylinder contains $3, 2, 3, 2$ from bottom to top.
• After inserting the $5$-th ball, the cylinder momentarily has $3, 2, 3, 2, 2$ from bottom to top. The two consecutive balls with $2$ disappear, and the cylinder eventually contains $3, 2, 3$ from bottom to top.

10
2 3 2 3 3 3 2 3 3 2

1
2
3
4
5
3
2
3
1
0