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:
PYTHON3 solution for "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...":
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.
 def solve(n,rat,s):
    count = n
    rec = dict()
    j = 0
    for i in rat:
        rec[i] = [j,s[j]]
        j+=1
    new_rat = [0]*count
    i = n
    while i>0:
        k = rec[i]
        if k[1] == '1':
            new_rat[k[0]] = count
            count-=1
            i-=1
        else:
            i-=1

    i = n
    while i>0:
        k = rec[i]
        if k[1] == '0':
            new_rat[k[0]] = count
            count-=1
            i-=1
        else:
            i-=1


    return new_rat

t = int(input())
for _ in range(t):
    n = int(input())
    rat = [int(i) for i in input().split()]
    s = input()
    ans = solve(n,rat,s)
    for i in ans:
        print(i,end=" ")
    print()