human
What is a Python program to find the one that has the smallest value of ∑_{i=1}^n |p_i-q_i|, where |x| is an absolute value of x given the following:
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 ≤ p_i ≤ 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, ..., q_n still form a permutation (1 ≤ q_i ≤ 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 ∑_{i=1}^n |p_i-q_i|, where |x| is an absolute value of x.

Print the permutation q_1, q_2, ..., q_n. If there are multiple answers, you can print any of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.

The first line of each testcase contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of songs.

The second line of each testcase contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ 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 ⋅ 10^5.

Output

For each testcase, print a permutation q — the re-evaluated ratings of the songs. If there are multiple answers such that ∑_{i=1}^n |p_i-q_i| is minimum possible, you can print any of them.

Example

Input

3
2
1 2
10
3
3 1 2
111
8
2...
Using python3 can you solve the prior task?
assistant
#Here is Python program to find the one that has the smallest value of ∑_{i=1}^n |p_i-q_i|, where |x| is an absolute value of x.

import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
sys.setrecursionlimit(10**5)

def bootstrap(f,stack=[]):
    def fun(*args,**kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to=next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to=stack[-1].send(to)
            return to
    return fun

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
 ...