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 3 1 8 5 4 7 6
01110001


Output


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. ∑_{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.
1
7
1 2 3 4 5 6 7
0101010
 3
2
1 2
10
7
1 2 3 4 5 6 7
0101010
8
2 3 1 8 5 4 7 6
01110001
 1
50
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
10101010101010101010101010101010101010101010101010

1 5 2 6 3 7 4
 2 1
1 5 2 6 3 7 4
1 6 5 8 3 2 4 7
 26 1 27 2 28 3 29 4 30 5 31 6 32 7 33 8 34 9 35 10 36 11 37 12 38 13 39 14 40 15 41 16 42 17 43 18 44 19 45 20 46 21 47 22 48 23 49 24 50 25

from __future__ import division, print_function

import os,sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip

from bisect import bisect_left as lower_bound, bisect_right as upper_bound 
def so():  return int(input())
def st():  return input()
def mj():  return map(int,input().strip().split(" "))
def msj(): return (map(str,input().strip().split(" ")))
def le():  return list(map(int,input().split()))
def rc():  return map(float,input().split())
def lebe():return list(map(int, input()))

def dmain():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()
def joro(L):
    return(''.join(map(str, L)))


def decimalToBinary(n): return bin(n).replace("0b","")


def isprime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
    return True
def npr(n, r):
    return factorial(n) // factorial(n - r) if n >= r else 0
 
 
def ncr(n, r):
    return factorial(n) // (factorial(r) * factorial(n - r)) if n >= r else 0
 
 
def lower_bound(li, num):
    answer = -1
    start = 0
    end = len(li) - 1
 
    while (start <= end):
        middle = (end + start) // 2
        if li[middle] >= num:
            answer = middle
            end = middle - 1
        else:
            start = middle + 1
    return answer  # min index where x is not less than num
 
 
def upper_bound(li, num):
    answer = -1
    start = 0
    end = len(li) - 1
 
    while (start <= end):
        middle = (end + start) // 2
 
        if li[middle] <= num:
            answer = middle
            start = middle + 1
 
        else:
            end = middle - 1
    return answer  # max index where x is not greater than num
def tir(a,b,c):
    if(0==c):
        return 1
    if(len(a)<=b):
        return 0
    
    if(c!=-1):
        return (tir(a,1+b,c+a[b]) or tir(a,b+1,c-a[b]) or tir(a,1+b,c)) 
        
        
    else:
        return (tir(a,1+b,a[b]) or tir(a,b+1,-a[b]) or tir(a,1+b,-1))
hoi=int(2**20)        
 
def abs(x):
    return x if x >= 0 else -x
 
 
def binary_search(li, val, lb, ub):
    # print(lb, ub, li)
    ans = -1
    while (lb <= ub):
        mid = (lb + ub) // 2
        # print('mid is',mid, li[mid])
        if li[mid] > val:
            ub = mid - 1
        elif val > li[mid]:
            lb = mid + 1
        else:
            ans = mid  # return index
            break
    return ans
 
 
def kadane(x):  # maximum sum contiguous subarray
    sum_so_far = 0
    current_sum = 0
    for i in x:
        current_sum += i
        if current_sum < 0:
            current_sum = 0
        else:
            sum_so_far = max(sum_so_far, current_sum)
    return sum_so_far

                    
def pref(li):
    pref_sum = [0]
    for i in li:
        pref_sum.append(pref_sum[-1] + i)
    return pref_sum
 

        
        
def SieveOfEratosthenes(n):
    prime = [True for i in range(n + 1)]
    p = 2
    li = []
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1
 
    for p in range(2, len(prime)):
        if prime[p]:
            li.append(p)
    return li
 
 
def primefactors(n):
    factors = []
    while (n % 2 == 0):
        factors.append(2)
        n //= 2
    for i in range(3, int(sqrt(n)) + 1, 2):  # only odd factors left
        while n % i == 0:
            factors.append(i)
            n //= i
    if n > 2:  # incase of prime
        factors.append(n)
    return factors
         
    
def read():
    sys.stdin  = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 
def tr(n):
    return n*(n+1)//2
boi=int(1e9-7)
doi=int(1e9+7)
def hup(x, y):
    "Calculate (x ** y) % z efficiently."
    number = 1
    while y:
        if y & 1:
            number = number * x % doi
        y >>= 1
        x = x * x % doi
    return number

y="YES"
n="NO"





    
def iu():
    import sys
    import math as my
    input=sys.stdin.readline
    d=[]
    e=[]
    m=so()
    L=le()
    M=[0]*m
    t=st()
    for i in range(len(t)):
        if(t[i]=='0'):
            d.append([L[i],i])
        else:
            e.append([L[i],i])
    d.sort()
    e.sort()
    k=1
    for i in range(len(d)):
        M[d[i][1]]=k
        k+=1
    for i in range(len(e)):
        M[e[i][1]]=k
        k+=1
    print(*M)
    
    
        
    
    
            
def main():
    for i in range(so()):
        iu()
        
    
    
    
    
    
    
    
    
    
    

    

    
        
        
            
    
    
                
            
                
                
                
                
            
    
            
            
    
    
    
    
        
            
    
           
            
            
        
    
        
    
    
        
        
        

            
                    
                
                    
                    
                    
                    
                    
                    
        
                
        
        
       
    
           
          
          
                
            
        
                
    
        
        
        
       
            
                
        




# region fastio
# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py

BUFSIZE = 8192


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"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion


if __name__ == "__main__":
    #read()
    main()
    #dmain()

# Comment Read()