An arcade game player wants to climb to the top of the leaderboard and track their ranking. The game uses Dense Ranking, so its leaderboard works like this:

The player with the highest score is ranked number $1$ on the leaderboard.
Players who have equal scores receive the same ranking number, and the next player(s) receive the immediately following ranking number.

Example

$ranked=[100,90,90,80]$

$player=[70,80,105]$

The ranked players will have ranks $1$, $2$, $2$, and $3$, respectively. If the player's scores are $70$, $\textbf{80}$ and $105$, their rankings after each game are $4^{th}$, $3^{rd}$ and $1^{st}$. Return $[4,3,1]$.

Function Description

Complete the climbingLeaderboard function in the editor below.

climbingLeaderboard has the following parameter(s):

int ranked[n]: the leaderboard scores
int player[m]: the player's scores

Returns

int[m]: the player's rank after each new score

Input Format

The first line contains an integer $n$, the number of players on the leaderboard.

The next line contains $n$ space-separated integers $\textit{ranked[i]}$, the leaderboard scores in decreasing order.

The next line contains an integer, $m$, the number games the player plays.

The last line contains $m$ space-separated integers $\textit{player}[j]$, the game scores.

Constraints

$1\leq n\leq2\times10^5$
$1\leq m\leq2\times10^5$
$0\leq\textit{ranked[i]}\leq10^9$ for $0\leq i<n$
$0\leq\textit{player}[j]\leq10^9$ for $0\leq j\lt m$
The existing leaderboard, $\textit{ranked}$, is in descending order.
The player's scores, $\textit{player}$, are in ascending order.

Subtask

For $\textbf{60\%}$ of the maximum score:

$1\leq n\leq200$
$1\leq m\leq200$

Sample Input 1

7
100 100 50 40 40 20 10
4
5 25 50 120

Sample Output 1

6
4
2
1

Explanation 1

Alice starts playing with $7$players already on the leaderboard, which looks like this:

After Alice finishes game $0$, her score is $5$and her ranking is $6$:

After Alice finishes game $1$, her score is $25$and her ranking is $4$:

After Alice finishes game $2$, her score is $50$and her ranking is tied with Caroline at $2$:

After Alice finishes game $3$, her score is $120$and her ranking is $1$:

Sample Input 2

6
100 90 90 80 75 60
5
50 65 77 90 102

Sample Output 2

6
5
4
2
1

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