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.*;

import static java.lang.Math.*;
import static java.lang.Math.ceil;
import static java.util.Arrays.sort;

public class C {
    static int mod = 1000000007;

    public static void main(String[] args) throws Exception {

        int test = ri();
        while (test-- > 0) {
            int n = ri();
            int a[] = ria(n);
            char c[] = rcha();
            int cnt = 0;
            List<Integer> zeros = new ArrayList<>();
            List<Integer> ones = new ArrayList<>();
            boolean isdiss = false;
            for (int i = 0; i < n; i++) {
                if (c[i] == '0') {
                    zeros.add(a[i]);
                    isdiss = true;
                } else {
                    cnt++;

                    ones.add(a[i]);
                }
            }
            if (isdiss){
                Collections.sort(ones);
                Collections.sort(zeros);
                HashMap<Integer, Integer> values = new HashMap<>();
                int size1 = zeros.size(), size2 = ones.size();
                for (int i = 0; i < size1; i++) {
                    values.put(zeros.get(i), (i + 1));
                }
                cnt++;
                for (int i = 0; i < size2; i++) {
                    values.put(ones.get(i), cnt++);
                }
                StringBuilder ans = new StringBuilder();
                for (int i = 0; i < n; i++) {
                    ans.append(values.get(a[i])).append(" ");
                }
                prln(ans);
            }else{
                prln(a);
            }

        }


        close();
    }


    static class Nodes {
        long a;
        int b;


        Nodes(long a, int b) {
            this.a = a;
            this.b = b;

        }


    }

    static class DisjointSetUnion {
        int p[];
        int count[];

        public DisjointSetUnion(int n) {
            p = new int[n];
            count = new int[n];
            for (int i = 0; i < n; i++) {
                count[i] = 1;
            }
            clear(n);
        }

        public void clear(int n) {
            for (int i = 0; i < n; i++) {
                p[i] = i;
            }
        }

        public int get(int x) {
            return x != p[x] ? p[x] = get(p[x]) : x;
        }

        public int getCount(int x) {
            return count[x];
        }

        public boolean union(int a, int b) {
            a = get(a);
            b = get(b);
            p[a] = b;
            if (a != b) {
                count[b] += count[a];
                count[a] = 0;
            }
            return a != b;
        }
    }

    static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static boolean[] isPrime;
    static Random __r = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final long LMAX = 9223372036854775807L;

    // math util
    static int minof(int a, int b, int c) {
        return min(a, min(b, c));
    }

    static int minof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        int min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static long minof(long a, long b, long c) {
        return min(a, min(b, c));
    }

    static long minof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        long min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static int maxof(int a, int b, int c) {
        return max(a, max(b, c));
    }

    static int maxof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        int max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static long maxof(long a, long b, long c) {
        return max(a, max(b, c));
    }

    static long maxof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        long max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static int powi(int a, int b) {
        if (a == 0) return 0;
        int ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static long powl(long a, int b) {
        if (a == 0) return 0;
        long ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static int fli(double d) {
        return (int) d;
    }

    static int cei(double d) {
        return (int) ceil(d);
    }

    static long fll(double d) {
        return (long) d;
    }

    static long cel(double d) {
        return (long) ceil(d);
    }

    static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static int[] exgcd(int a, int b) {
        if (b == 0) return new int[]{1, 0};
        int[] y = exgcd(b, a % b);
        return new int[]{y[1], y[0] - y[1] * (a / b)};
    }

    static long[] exgcd(long a, long b) {
        if (b == 0) return new long[]{1, 0};
        long[] y = exgcd(b, a % b);
        return new long[]{y[1], y[0] - y[1] * (a / b)};
    }

    static int randInt(int min, int max) {
        return __r.nextInt(max - min + 1) + min;
    }

    static long mix(long x) {
        x += 0x9e3779b97f4a7c15L;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
        x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
        return x ^ (x >> 31);
    }

    static void setTrue(int n) {
        for (int i = 0; i < n; i++) {
            isPrime[i] = true;
        }
    }

    static void prime(int n) {
        for (int i = 2; i * i < n; i++) {
            if (isPrime[i]) {
                for (int j = i * i; j < n; j += i) isPrime[j] = false;
            }
        }
    }

    public static long lcm(long number1, long number2) {
        if (number1 == 0 || number2 == 0) {
            return 0;
        }
        long absNumber1 = Math.abs(number1);
        long absNumber2 = Math.abs(number2);
        long absHigherNumber = Math.max(absNumber1, absNumber2);
        long absLowerNumber = Math.min(absNumber1, absNumber2);
        long lcm = absHigherNumber;
        while (lcm % absLowerNumber != 0) {
            lcm += absHigherNumber;
        }
        return lcm;
    }

    // array util
    static void reverse(int[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            int swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(long[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            long swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(double[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            double swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(char[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            char swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void shuffle(int[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            int swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(long[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            long swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(double[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            double swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void rsort(int[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(long[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(double[] a) {
        shuffle(a);
        sort(a);
    }

    static int[] copy(int[] a) {
        int[] ans = new int[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static long[] copy(long[] a) {
        long[] ans = new long[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static double[] copy(double[] a) {
        double[] ans = new double[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static char[] copy(char[] a) {
        char[] ans = new char[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static void resetBoolean(boolean[] vis, int n) {
        for (int i = 0; i < n; i++) {
            vis[i] = false;
        }
    }

    static void setMinusOne(int[][] matrix) {
        int row = matrix.length;
        int col = matrix[0].length;

        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                matrix[i][j] = -1;
            }
        }

    }

    // input
    static void r() throws IOException {
        input = new StringTokenizer(rline());
    }

    static int ri() throws IOException {
        return Integer.parseInt(rline().split(" ")[0]);
    }

    static long rl() throws IOException {
        return Long.parseLong(rline());
    }

    static double rd() throws IOException {
        return Double.parseDouble(rline());
    }

    static int[] ria(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni();
        return a;
    }

    static void ria(int[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = ni();
    }

    static int[] riam1(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni() - 1;
        return a;
    }

    static void riam1(int[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = ni() - 1;
    }

    static long[] rla(int n) throws IOException {
        long[] a = new long[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nl();
        return a;
    }

    static void rla(long[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = nl();
    }

    static double[] rda(int n) throws IOException {
        double[] a = new double[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nd();
        return a;
    }

    static void rda(double[] a) throws IOException {
        int n = a.length;
        r();
        for (int i = 0; i < n; ++i) a[i] = nd();
    }

    static char[] rcha() throws IOException {
        return rline().toCharArray();
    }

    static void rcha(char[] a) throws IOException {
        int n = a.length, i = 0;
        for (char c : rline().toCharArray()) a[i++] = c;
    }

    static String rline() throws IOException {
        return __i.readLine();
    }

    static String n() {
        return input.nextToken();
    }

    static int rni() throws IOException {
        r();
        return ni();
    }

    static int ni() {
        return Integer.parseInt(n());
    }

    static long rnl() throws IOException {
        r();
        return nl();
    }

    static long nl() {
        return Long.parseLong(n());
    }

    static double rnd() throws IOException {
        r();
        return nd();
    }

    static double nd() {
        return Double.parseDouble(n());
    }

    // output
    static void pr(int i) {
        __o.print(i);
    }

    static void prln(int i) {
        __o.println(i);
    }

    static void pr(long l) {
        __o.print(l);
    }

    static void prln(long l) {
        __o.println(l);
    }

    static void pr(double d) {
        __o.print(d);
    }

    static void prln(double d) {
        __o.println(d);
    }

    static void pr(char c) {
        __o.print(c);
    }

    static void prln(char c) {
        __o.println(c);
    }

    static void pr(char[] s) {
        __o.print(new String(s));
    }

    static void prln(char[] s) {
        __o.println(new String(s));
    }

    static void pr(String s) {
        __o.print(s);
    }

    static void prln(String s) {
        __o.println(s);
    }

    static void pr(Object o) {
        __o.print(o);
    }

    static void prln(Object o) {
        __o.println(o);
    }

    static void prln() {
        __o.println();
    }

    static void pryes() {
        prln("yes");
    }

    static void pry() {
        prln("Yes");
    }

    static void prY() {
        prln("YES");
    }

    static void prno() {
        prln("no");
    }

    static void prn() {
        prln("No");
    }

    static void prN() {
        prln("NO");
    }

    static boolean pryesno(boolean b) {
        prln(b ? "yes" : "no");
        return b;
    }

    ;

    static boolean pryn(boolean b) {
        prln(b ? "Yes" : "No");
        return b;
    }

    static boolean prYN(boolean b) {
        prln(b ? "YES" : "NO");
        return b;
    }

    static void prln(int... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(long... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(double... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static <T> void prln(Collection<T> c) {
        int n = c.size() - 1;
        Iterator<T> iter = c.iterator();
        for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i) ;
        if (n >= 0) prln(iter.next());
        else prln();
    }

    static void h() {
        prln("hlfd");
        flush();
    }

    static void flush() {
        __o.flush();
    }

    static void close() {
        __o.close();
    }

}
