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

import java.io.*;
import java.util.*;

public class Main {
    
    InputStream is;
    FastWriter out;
    String INPUT = "";

    void run() throws Exception
    {
        is = System.in;
        out = new FastWriter(System.out);
        solve();
        out.flush();
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
 
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int[] na2(int n)
    {
        int[] a = new int[n+1];
        a[0] = 0;
        for(int i = 1;i <= n;i++)a[i] = ni();
        return a;
    }
 
    private long[] nal(int n)
    {
        long[] a = new long[n];
        for(int i = 0;i < n;i++)a[i] = nl();
        return a;
    }
 
    private long[] nal2(int n)
    {
        long[] a = new long[n+1];
        a[0] = 0L;
        for(int i = 1;i <= n;i++)a[i] = nl();
        return a;
    }
 
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
 
    private int[][] nmi(int n, int m) {
        int[][] map = new int[n][];
        for(int i = 0;i < n;i++)map[i] = na(m);
        return map;
    }
 
    private int ni() { return (int)nl(); }
 
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
 
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private int gcd(int a, int b) {
        if(b == 0)
            return a;
        if(a == 0)
            return b;
        return gcd(b, a%b);
    }

    private int gcdRange(int l, int r) {
        int ans = 1;
        for (int i = r; i >= 1; i--) {
            if ((r / i) - (l - 1) / i > 1) {
                ans = i;
                break;
            }
        }
        return ans;
    }

    // ∑i = gcd(a1,a2,... ,ai) = gcd(a1) + gcd(a1,a2) + gcd(a1,a2,a3) + gcd(a1,a2,a3,a4) + .............;
    private void gcdPrefix(int[] a, int n) {
        int[] f = new int[5000001];
        for(int v : a) f[v]++;
        for(int i = 1;i <= 5000000;i++){
            for(int j = i*2;j <= 5000000;j+=i){
                f[i] += f[j];
            }
        }
        long[] dp = new long[5000001];
        long ans = 0;
        for(int i = 5000000;i >= 1;i--){
            dp[i] = (long)f[i] * i;
            for(int j = i*2;j <= 5000000;j+=i){
                dp[i] = Math.max(dp[i], dp[j] + (long)(f[i] - f[j]) * i);
            }
            ans = Math.max(ans, dp[i]);
        }
        out.println(ans);
    }

    private int findTrailingZerosInFactorial(int n)
    {
    //  5 -> 1 , 10 -> 2 , 20 -> 4 , 100 -> 24
        if (n < 0)
            return -1;
        int count = 0;
        for (int i = 5; n / i >= 1; i *= 5)
            count += n / i;
 
        return count;
    }

    private void LongestX() {
//  Given is a string S consisting of X and ..
//  You can do the following operation on S between 0 and K times (inclusive).
//  Replace a . with an X.
//  What is the maximum possible number of consecutive Xs in S after the operations?
        char[] s = ns().toCharArray();
        int K = ni();
        int n = s.length;
        int[] cum = new int[n+1];
        cum[0] = 0;
        for(int i = 0;i < n;i++){
            cum[i+1] = cum[i] + (s[i] == '.' ? 1 : 0);
        }
 
        int low = -1;
        int high = s.length + 1;
        outer:
        while(high - low > 1){
            int h = high + low >> 1;
            for(int i = 0;i+h <= n;i++){
                if(cum[i+h] - cum[i] <= K){
                    low = h;
                    continue outer;
                }
            }
            high = h;
        }
        out.println(low);
    }

    private long calculate_Xor(long n) 
    {
        if(n%4 == 0) return n;
        else if(n%4 == 1) return 1;
        else if(n%4 == 2) return n+1;
        return 0;
    }

    private class Pair {
        int first;
        int second;
        Pair(int a, int b)
        {
            first = a;
            second = b;
        }
    }

    private String swap(String s , int i , int j ) 
    {
        StringBuilder str = new StringBuilder(s);
        char l = str.charAt(i) , r = str.charAt(j);
        str.setCharAt(i,r);
        str.setCharAt(j,l);
        return str.toString();
    }
/*****************************************************************************************************/
    void solve()
    {
        int t = ni();
        while(t-- > 0)
        {
            int n = ni();
            int a[] = new int[n];
            int b[] = new int[n];
            Map<Integer,Integer> map = new HashMap<>();
            ArrayList<Integer> ones = new ArrayList<>();
            ArrayList<Integer> zeroes = new ArrayList<>();
            for(int i=0; i<n; i++)
            {
                a[i] = ni();
                b[i] = a[i];
                map.put(a[i], i);
            }
            String s = ns();
     
            for(int i=0;i<n;i++)
            {
                if(s.charAt(i)=='0')
                    zeroes.add(a[i]);
                else
                    ones.add(a[i]);
            }
            Collections.sort(ones, Collections.reverseOrder());
            Collections.sort(zeroes, Collections.reverseOrder());

            int i;
            for(i=0; i<ones.size(); i++)
            {
                b[map.get(ones.get(i))] = a[i];
            }
            for(int j=0; j<zeroes.size(); j++)
            {
                b[map.get(zeroes.get(j))] = a[i];
                i++;
            }
     
            for(int k=0; k<n; k++)
                out.print(b[k]+" ");
            out.println();
        }
    }
/******************************************************************************************************/ 
    public static class FastWriter
    {
        private static final int BUF_SIZE = 1<<13;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;
 
        private FastWriter(){out = null;}
 
        public FastWriter(OutputStream os)
        {
            this.out = os;
        }
 
        public FastWriter(String path)
        {
            try {
                this.out = new FileOutputStream(path);
            } catch (FileNotFoundException e) {
                throw new RuntimeException("FastWriter");
            }
        }
 
        public FastWriter write(byte b)
        {
            buf[ptr++] = b;
            if(ptr == BUF_SIZE)innerflush();
            return this;
        }
 
        public FastWriter write(char c)
        {
            return write((byte)c);
        }
 
        public FastWriter write(char[] s)
        {
            for(char c : s){
                buf[ptr++] = (byte)c;
                if(ptr == BUF_SIZE)innerflush();
            }
            return this;
        }
 
        public FastWriter write(String s)
        {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte)c;
                if(ptr == BUF_SIZE)innerflush();
            });
            return this;
        }
 
        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }
 
        public FastWriter write(int x)
        {
            if(x == Integer.MIN_VALUE){
                return write((long)x);
            }
            if(ptr + 12 >= BUF_SIZE)innerflush();
            if(x < 0){
                write((byte)'-');
                x = -x;
            }
            int d = countDigits(x);
            for(int i = ptr + d - 1;i >= ptr;i--){
                buf[i] = (byte)('0'+x%10);
                x /= 10;
            }
            ptr += d;
            return this;
        }
 
        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }
 
        public FastWriter write(long x)
        {
            if(x == Long.MIN_VALUE){
                return write("" + x);
            }
            if(ptr + 21 >= BUF_SIZE)innerflush();
            if(x < 0){
                write((byte)'-');
                x = -x;
            }
            int d = countDigits(x);
            for(int i = ptr + d - 1;i >= ptr;i--){
                buf[i] = (byte)('0'+x%10);
                x /= 10;
            }
            ptr += d;
            return this;
        }
 
        public FastWriter write(double x, int precision)
        {
            if(x < 0){
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision)/2;
            //      if(x < 0){ x = 0; }
            write((long)x).write(".");
            x -= (long)x;
            for(int i = 0;i < precision;i++){
                x *= 10;
                write((char)('0'+(int)x));
                x -= (int)x;
            }
            return this;
        }
 
        public FastWriter writeln(char c){
            return write(c).writeln();
        }
 
        public FastWriter writeln(int x){
            return write(x).writeln();
        }
 
        public FastWriter writeln(long x){
            return write(x).writeln();
        }
 
        public FastWriter writeln(double x, int precision){
            return write(x, precision).writeln();
        }
 
        public FastWriter write(int... xs)
        {
            boolean first = true;
            for(int x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }
 
        public FastWriter write(long... xs)
        {
            boolean first = true;
            for(long x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }
 
        public FastWriter writeln()
        {
            return write((byte)'\n');
        }
 
        public FastWriter writeln(int... xs)
        {
            return write(xs).writeln();
        }
 
        public FastWriter writeln(long... xs)
        {
            return write(xs).writeln();
        }
 
        public FastWriter writeln(char[] line)
        {
            return write(line).writeln();
        }
 
        public FastWriter writeln(char[]... map)
        {
            for(char[] line : map)write(line).writeln();
            return this;
        }
 
        public FastWriter writeln(String s)
        {
            return write(s).writeln();
        }
 
        private void innerflush()
        {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }
 
        public void flush()
        {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }
 
        public FastWriter print(byte b) { return write(b); }
        public FastWriter print(char c) { return write(c); }
        public FastWriter print(char[] s) { return write(s); }
        public FastWriter print(String s) { return write(s); }
        public FastWriter print(int x) { return write(x); }
        public FastWriter print(long x) { return write(x); }
        public FastWriter print(double x, int precision) { return write(x, precision); }
        public FastWriter println(char c){ return writeln(c); }
        public FastWriter println(int x){ return writeln(x); }
        public FastWriter println(long x){ return writeln(x); }
        public FastWriter println(double x, int precision){ return writeln(x, precision); }
        public FastWriter print(int... xs) { return write(xs); }
        public FastWriter print(long... xs) { return write(xs); }
        public FastWriter println(int... xs) { return writeln(xs); }
        public FastWriter println(long... xs) { return writeln(xs); }
        public FastWriter println(char[] line) { return writeln(line); }
        public FastWriter println(char[]... map) { return writeln(map); }
        public FastWriter println(String s) { return writeln(s); }
        public FastWriter println() { return writeln(); }
    }
 
    public void trnz(int... o)
    {
        for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
        System.out.println();
    }
 
    // print ids which are 1
    public void trt(long... o)
    {
        Queue<Integer> stands = new ArrayDeque<>();
        for(int i = 0;i < o.length;i++){
            for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
        }
        System.out.println(stands);
    }
 
    public void tf(boolean... r)
    {
        for(boolean x : r)System.out.print(x?'#':'.');
        System.out.println();
    }
 
    public void tf(boolean[]... b)
    {
        for(boolean[] r : b) {
            for(boolean x : r)System.out.print(x?'#':'.');
            System.out.println();
        }
        System.out.println();
    }
 
    public void tf(long[]... b)
    {
        if(INPUT.length() != 0) {
            for (long[] r : b) {
                for (long x : r) {
                    for (int i = 0; i < 64; i++) {
                        System.out.print(x << ~i < 0 ? '#' : '.');
                    }
                }
                System.out.println();
            }
            System.out.println();
        }
    }
 
    public void tf(long... b)
    {
        if(INPUT.length() != 0) {
            for (long x : b) {
                for (int i = 0; i < 64; i++) {
                    System.out.print(x << ~i < 0 ? '#' : '.');
                }
            }
            System.out.println();
        }
    }
}