Problem Statement

$K$ has come to a game tournament.
In this game, the goal is to get as high a score as possible.
$N$ people, including $K$, are participating.
They play $1$ time each in order, and the ranking is updated as they go.

$K$ plays first.
Find $K$'s rank at the moment each person finishes playing.
A higher score gives a higher rank.
In the case of a tie, the person who played earlier ranks higher.

Input

$N$
$a_0$
$a_1$
$\dots$
$a_{N-1}$

The $1$st line gives $N$.
The $2$nd and subsequent lines give each person's score $a_i$.
$a_0$ represents $K$'s score.

All input is given as integers.
$1 \le N \le 10^5$
$1 \le a_i \le 10^9$

Output

Output $K$'s rank at each point in time, over $N$ lines.

Sample

3
2
3
1

1
2
2

6
1
1
4
5
1
4

1
1
2
3
3
4