Problem: You are given a binary string s consisting of n zeros and ones.

Your task is to divide the given string into the minimum number of subsequences in such a way that each character of the string belongs to exactly one subsequence and each subsequence looks like "010101 ..." or "101010 ..." (i.e. the subsequence should not contain two adjacent zeros or ones).

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, subsequences of "1011101" are "0", "1", "11111", "0111", "101", "1001", but not "000", "101010" and "11100".

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of s. The second line of the test case contains n characters '0' and '1' — the string s.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer: in the first line print one integer k (1 ≤ k ≤ n) — the minimum number of subsequences you can divide the string s to. In the second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the number of subsequence the i-th character of s belongs to.

If there are several answers, you can print any.

Example

Input


4
4
0011
6
111111
5
10101
8
01010000


Output


2
1 2 2 1 
6
1 2 3 4 5 6 
1
1 1 1 1 1 
4
1 1 1 1 1 2 3 4 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.BitSet;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        Scanner in = new Main().new Scanner(inputStream);
        Main solver = new Main();
        solver.run(in);
    }

    public void runn(Scanner in) {
        int n = in.ni();
        String line = in.rl();

        LinkedList<LinkedList<Integer>> ones = new LinkedList<>();
        LinkedList<LinkedList<Integer>> zeroes = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            if (line.charAt(i) == '1') {
                if (zeroes.isEmpty()) {
                    LinkedList<Integer> ll = new LinkedList<>();
                    ll.add(i);
                    ones.push(ll);
                } else {
                    LinkedList<Integer> z = zeroes.pop();
                    z.add(i);
                    ones.push(z);
                }
            } else {
                if (ones.isEmpty()) {
                    LinkedList<Integer> ll = new LinkedList<>();
                    ll.add(i);
                    zeroes.push(ll);
                } else {
                    LinkedList<Integer> z = ones.pop();
                    z.add(i);
                    zeroes.push(z);
                }
            }
        }
        int[] pos = new int[n];
        int id = 1;
        while (!ones.isEmpty()) {
            LinkedList<Integer> top = ones.pop();
            while (!top.isEmpty())
                pos[top.pop()] = id;
            id++;
        }

        while (!zeroes.isEmpty()) {
            LinkedList<Integer> top = zeroes.pop();
            while (!top.isEmpty())
                pos[top.pop()] = id;
            id++;
        }

        System.out.println(id - 1);
        for (int i = 0; i < n; i++)
            System.out.print(pos[i] + " ");
        System.out.println();
    }

    class Scanner {
        BufferedReader br;
        StringTokenizer in;

        public Scanner(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            return hasMoreTokens() ? in.nextToken() : null;
        }

        public String rl() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                return null;
            }
        }

        boolean hasMoreTokens() {
            while (in == null || !in.hasMoreTokens()) {
                String s = rl();
                if (s == null)
                    return false;
                in = new StringTokenizer(s);
            }
            return true;
        }

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

        public int ni() {
            return Integer.parseInt(nextString());
        }

        public double nd() {
            return Double.parseDouble(nextString());
        }

        public long nl() {
            return Long.parseLong(nextString());
        }

        public int[] nia(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] nla(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

    }

    int stoi(String a) {
        return Integer.parseInt(a);
    }

    void debug(int[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(long[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    void debug(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++)
                System.out.print(arr[i][j] + "\t");
            System.out.println();
        }
    }

    void run(Scanner in) {
        int t = in.ni();
        while (t-- > 0)
            runn(in);
    }

    class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        public int compareTo(Pair other) {
            if (b == other.b)
                return Long.compare(a, other.a);
            else
                return Long.compare(b, other.b);
        }

        public int hashCode() {
            return (int) (a * 100007 + b);
        }

        public boolean equals(Object other) {
            Pair o = (Pair) other;
            return a == o.a && b == o.b;
        }
    }
}