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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Jatin Yadav
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    D solver = new D();
    solver.solve(1, in, out);
    out.close();
  }

  static class D {
    InputReader in;
    PrintWriter out;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
      this.in = in;
      this.out = out;
      int t = ni();
      for (int i = 0; i < t; i++)
        solve();
    }

    public void solve() {
      int n = ni();
      char[] a = in.next().toCharArray();
      ArrayDeque<Integer> zs = new ArrayDeque<>(),
          os = new ArrayDeque<>();
      int[] ans = new int[n];
      int nPiles = 0;
      int index = 0;
      for (char c : a) {
        if (c == '0') {
          if (zs.isEmpty()) {
            nPiles++;
            ans[index] = nPiles;
            os.addLast(nPiles);
          } else {
            int p = zs.removeFirst();
            ans[index] = p;
            os.addLast(p);
          }
        } else {
          if (os.isEmpty()) {
            nPiles++;
            ans[index] = nPiles;
            zs.addLast(nPiles);
          } else {
            int p = os.removeFirst();
            ans[index] = p;
            zs.addLast(p);
          }
        }
        index++;
      }
      out.println(nPiles);
      for (
          int i : ans)
        out.print(i + " ");
      out.println();
    }

    private int ni() {
      return in.nextInt();
    }
  }

  static class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar;
    private int snumChars;
    private InputReader.SpaceCharFilter filter;

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

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

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

    public String next() {
      int c = snext();
      while (isSpaceChar(c)) {
        c = snext();
      }
      StringBuilder res = new StringBuilder();
      do {
        res.appendCodePoint(c);
        c = snext();
      } while (!isEndOfLine(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public boolean isEndOfLine(int c) {
      return c == '\n' || c == '\r' || c == -1;
    }

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