human
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...
t=int
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.
(input().strip())
for val in range(t):
    n=int(input().strip())
    class data:
        def __init__(self,x):
            self.x=x
            self.y=None
        def __repr__(self):
            return "({},{})".format(self.x,self.y)
            
    p=[data(int(x)) for x in input().strip().split(" ")]
    s=input().strip()
    liked=[]
    disliked=[]
    for i in range(n):
        if s[i]=="1":
            liked.extend([p[i]])
        else:
            disliked.extend([p[i]])
    #print(liked)
    #print(disliked)
            
    def Bsort(L,n):
        X=[None for i in range(n)]
        for val in L:
            X[(val.x-1)%n]=val
        Y=[]
        for i in X:
            if i!=None :
                Y.extend([i])
        return Y 
    liked=Bsort(liked,n)
    disliked=Bsort(disliked,n)
    disliked.extend(liked)
    
    
    for i in range(n):
        disliked[i].y=i+1 
    #print(disliked)
    for i in p:
        print(i.y,end=" ")
    print()