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.*;

/**
 * Provide prove of correctness before implementation. Implementation can cost a lot of time.
 * Anti test that prove that it's wrong.
 * <p>
 * Do not confuse i j k g indexes, upTo and length. Do extra methods!!! Write more informative names to simulation
 * <p>
 * Will program ever exceed limit?
 * Try all approaches with prove of correctness if task is not obvious.
 * If you are given formula/rule: Try to play with it.
 * Analytic solution/Hardcoded solution/Constructive/Greedy/DP/Math/Brute force/Symmetric data
 * Number theory
 * Game theory (optimal play) that consider local and global strategy.
 */
public class B {

    private void solveOne() {
        int n = nextInt();

        int[] p = nextIntArr(n);
        char[] s = nextString().toCharArray();

        Comparator<Pair> co = Comparator.comparing(pair -> pair.val);
        Set<Pair> ordered = new TreeSet<>(co);
        for(int i = 0 ; i < n ; i ++){
            if(s[i] == '1') {
                ordered.add(new Pair(p[i], i));
            }
        }

        int[] ans = new int[n];
        int permNext = 1;
        for(Pair i : ordered) {
            ans[i.ind] = permNext++;
        }

        ordered = new TreeSet<>(co);
        for(int i = 0 ; i < n ; i ++){
            if(s[i] == '0') {
                ordered.add(new Pair(p[i], i));
            }
        }

        for(Pair i : ordered) {
            ans[i.ind] = permNext++;
        }

        System.out.println(ans);

    }

    class Pair{
        int val;
        int ind;

        public Pair(int val, int ind) {
            this.val = val;
            this.ind = ind;
        }
    }

    private void solve() {
        int t = System.in.readInt();
        for (int tt = 0; tt < t; tt++) {
            solveOne();
        }
    }

    class AssertionRuntimeException extends RuntimeException {

        AssertionRuntimeException(Object expected,
                                  Object actual, Object... input) {
            super("expected = " + expected + ",\n actual = " + actual + ",\n " + Arrays.deepToString(input));
        }
    }

    private int nextInt() {
        return System.in.readInt();
    }

    private long nextLong() {
        return System.in.readLong();
    }

    private String nextString() {
        return System.in.readString();
    }

    private int[] nextIntArr(int n) {
        return System.in.readIntArray(n);
    }

    private long[] nextLongArr(int n) {
        return System.in.readLongArray(n);
    }


    public static void main(String[] args) {
        new B().run();
    }

    static class System {
        private static FastInputStream in;
        private static FastPrintStream out;
    }

    private void run() {
        System.in = new FastInputStream(java.lang.System.in);
        System.out = new FastPrintStream(java.lang.System.out);
        solve();
        System.out.flush();
    }

    private static class FastPrintStream {
        private static final int BUF_SIZE = 8192;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;

        private FastPrintStream() {
            this(java.lang.System.out);
        }

        public FastPrintStream(OutputStream os) {
            this.out = os;
        }

        public FastPrintStream(String path) {
            try {
                this.out = new FileOutputStream(path);
            } catch (FileNotFoundException e) {
                throw new RuntimeException("FastWriter");
            }
        }

        public FastPrintStream print(byte b) {
            buf[ptr++] = b;
            if (ptr == BUF_SIZE) innerflush();
            return this;
        }

        public FastPrintStream print(char c) {
            return print((byte) c);
        }

        public FastPrintStream print(char[] s) {
            for (char c : s) {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            }
            return this;
        }

        public FastPrintStream print(String s) {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            });
            return this;
        }

        //can be optimized
        public FastPrintStream print0(char[] s) {
            if (ptr + s.length < BUF_SIZE) {
                for (char c : s) {
                    buf[ptr++] = (byte) c;
                }
            } else {
                for (char c : s) {
                    buf[ptr++] = (byte) c;
                    if (ptr == BUF_SIZE) innerflush();
                }
            }
            return this;
        }

        //can be optimized
        public FastPrintStream print0(String s) {
            if (ptr + s.length() < BUF_SIZE) {
                for (int i = 0; i < s.length(); i++) {
                    buf[ptr++] = (byte) s.charAt(i);
                }
            } else {
                for (int i = 0; i < s.length(); i++) {
                    buf[ptr++] = (byte) s.charAt(i);
                    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 FastPrintStream print(int x) {
            if (x == Integer.MIN_VALUE) {
                return print((long) x);
            }
            if (ptr + 12 >= BUF_SIZE) innerflush();
            if (x < 0) {
                print((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 FastPrintStream print(long x) {
            if (x == Long.MIN_VALUE) {
                return print("" + x);
            }
            if (ptr + 21 >= BUF_SIZE) innerflush();
            if (x < 0) {
                print((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 FastPrintStream print(double x, int precision) {
            if (x < 0) {
                print('-');
                x = -x;
            }
            x += Math.pow(10, -precision) / 2;
            //		if(x < 0){ x = 0; }
            print((long) x).print(".");
            x -= (long) x;
            for (int i = 0; i < precision; i++) {
                x *= 10;
                print((char) ('0' + (int) x));
                x -= (int) x;
            }
            return this;
        }

        public FastPrintStream println(int[] a, int from, int upTo, char separator) {
            for (int i = from; i < upTo; i++) {
                print(a[i]);
                print(separator);
            }
            print('\n');
            return this;
        }

        public FastPrintStream println(int[] a) {
            return println(a, 0, a.length, ' ');
        }

        public FastPrintStream println(char c) {
            return print(c).println();
        }

        public FastPrintStream println(int x) {
            return print(x).println();
        }

        public FastPrintStream println(long x) {
            return print(x).println();
        }

        public FastPrintStream println(String x) {
            return print(x).println();
        }

        public FastPrintStream println(double x, int precision) {
            return print(x, precision).println();
        }

        public FastPrintStream println() {
            return print((byte) '\n');
        }

        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");
            }
        }
    }

    private static class FastInputStream {
        private boolean finished = false;

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public FastInputStream(InputStream stream) {
            this.stream = stream;
        }

        public double[] readDoubleArray(int size) {
            double[] array = new double[size];
            for (int i = 0; i < size; i++) {
                array[i] = readDouble();
            }
            return array;
        }

        public String[] readStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; i++) {
                array[i] = readString();
            }
            return array;
        }

        public char[] readCharArray(int size) {
            char[] array = new char[size];
            for (int i = 0; i < size; i++) {
                array[i] = readCharacter();
            }
            return array;
        }

        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }

        public void readLongArrays(long[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readLong();
                }
            }
        }

        public void readDoubleArrays(double[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readDouble();
                }
            }
        }

        public char[][] readTable(int rowCount, int columnCount) {
            char[][] table = new char[rowCount][];
            for (int i = 0; i < rowCount; i++) {
                table[i] = this.readCharArray(columnCount);
            }
            return table;
        }

        public int[][] readIntTable(int rowCount, int columnCount) {
            int[][] table = new int[rowCount][];
            for (int i = 0; i < rowCount; i++) {
                table[i] = readIntArray(columnCount);
            }
            return table;
        }

        public double[][] readDoubleTable(int rowCount, int columnCount) {
            double[][] table = new double[rowCount][];
            for (int i = 0; i < rowCount; i++) {
                table[i] = this.readDoubleArray(columnCount);
            }
            return table;
        }

        public long[][] readLongTable(int rowCount, int columnCount) {
            long[][] table = new long[rowCount][];
            for (int i = 0; i < rowCount; i++) {
                table[i] = readLongArray(columnCount);
            }
            return table;
        }

        public String[][] readStringTable(int rowCount, int columnCount) {
            String[][] table = new String[rowCount][];
            for (int i = 0; i < rowCount; i++) {
                table[i] = this.readStringArray(columnCount);
            }
            return table;
        }

        public String readText() {
            StringBuilder result = new StringBuilder();
            while (true) {
                int character = read();
                if (character == '\r') {
                    continue;
                }
                if (character == -1) {
                    break;
                }
                result.append((char) character);
            }
            return result.toString();
        }

        public void readStringArrays(String[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readString();
                }
            }
        }

        public long[] readLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = readLong();
            }
            return array;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public int peekNonWhitespace() {
            while (isWhitespace(peek())) {
                read();
            }
            return peek();
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0) {
                s = readLine0();
            }
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines) {
                return readLine();
            } else {
                return readLine0();
            }
        }

        public char readCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public boolean isExhausted() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value == -1;
        }

        public String next() {
            return readString();
        }

        public SpaceCharFilter getFilter() {
            return filter;
        }

        public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

}