Berland Music
Description
Berland Music is a music streaming service built specifically to support Berland local artist. Its developers are currently working on a song recommendation module.
So imagine Monocarp got recommended $n$ songs, numbered from $1$ to $n$. The $i$-th song had its predicted rating equal to $p_i$, where $1 \le p_i \le n$ and every integer from $1$ to $n$ appears exactly once. In other words, $p$ is a permutation.
After listening to each of them, Monocarp pressed either a like or a dislike button. Let his vote sequence be represented with a string $s$, such that $s_i=0$ means that he disliked the $i$-th song, and $s_i=1$ means that he liked it.
Now the service has to re-evaluate the song ratings in such a way that:
- the new ratings $q_1, q_2, \dots, q_n$ still form a permutation ($1 \le q_i \le n$; each integer from $1$ to $n$ appears exactly once);
- every song that Monocarp liked should have a greater rating than every song that Monocarp disliked (formally, for all $i, j$ such that $s_i=1$ and $s_j=0$, $q_i>q_j$ should hold).
Among all valid permutations $q$ find the one that has the smallest value of $\sum\limits_{i=1}^n |p_i-q_i|$, where $|x|$ is an absolute value of $x$.
Print the permutation $q_1, q_2, \dots, q_n$. If there are multiple answers, you can print any of them.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of songs.
The second line of each testcase contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$) — the permutation of the predicted ratings.
The third line contains a single string $s$, consisting of $n$ characters. Each character is either a $0$ or a $1$. $0$ means that Monocarp disliked the song, and $1$ means that he liked it.
The sum of $n$ over all testcases doesn't exceed $2 \cdot 10^5$.
For each testcase, print a permutation $q$ — the re-evaluated ratings of the songs. If there are multiple answers such that $\sum\limits_{i=1}^n |p_i-q_i|$ is minimum possible, you can print any of them.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of songs.
The second line of each testcase contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$) — the permutation of the predicted ratings.
The third line contains a single string $s$, consisting of $n$ characters. Each character is either a $0$ or a $1$. $0$ means that Monocarp disliked the song, and $1$ means that he liked it.
The sum of $n$ over all testcases doesn't exceed $2 \cdot 10^5$.
Output
For each testcase, print a permutation $q$ — the re-evaluated ratings of the songs. If there are multiple answers such that $\sum\limits_{i=1}^n |p_i-q_i|$ is minimum possible, you can print any of them.
Samples
3
2
1 2
10
3
3 1 2
111
8
2 3 1 8 5 4 7 6
01110001
2 1
3 1 2
1 6 5 8 3 2 4 7
Note
In the first testcase, there exists only one permutation $q$ such that each liked song is rating higher than each disliked song: song $1$ gets rating $2$ and song $2$ gets rating $1$. $\sum\limits_{i=1}^n |p_i-q_i|=|1-2|+|2-1|=2$.
In the second testcase, Monocarp liked all songs, so all permutations could work. The permutation with the minimum sum of absolute differences is the permutation equal to $p$. Its cost is $0$.