Problem: The only difference between easy and hard versions is constraints.

There are n kids, each of them is reading a unique book. At the end of any day, the i-th kid will give his book to the p_i-th kid (in case of i = p_i the kid will give his book to himself). It is guaranteed that all values of p_i are distinct integers from 1 to n (i.e. p is a permutation). The sequence p doesn't change from day to day, it is fixed.

For example, if n=6 and p=[4, 6, 1, 3, 5, 2] then at the end of the first day the book of the 1-st kid will belong to the 4-th kid, the 2-nd kid will belong to the 6-th kid and so on. At the end of the second day the book of the 1-st kid will belong to the 3-th kid, the 2-nd kid will belong to the 2-th kid and so on.

Your task is to determine the number of the day the book of the i-th child is returned back to him for the first time for every i from 1 to n.

Consider the following example: p = [5, 1, 2, 4, 3]. The book of the 1-st kid will be passed to the following kids:

  * after the 1-st day it will belong to the 5-th kid, 
  * after the 2-nd day it will belong to the 3-rd kid, 
  * after the 3-rd day it will belong to the 2-nd kid, 
  * after the 4-th day it will belong to the 1-st kid. 



So after the fourth day, the book of the first kid will return to its owner. The book of the fourth kid will return to him for the first time after exactly one day.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 1000) — the number of queries. Then q queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of kids in the query. The second line of the query contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, all p_i are distinct, i.e. p is a permutation), where p_i is the kid which will get the book of the i-th kid.

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

Output

For each query, print the answer on it: n integers a_1, a_2, ..., a_n, where a_i is the number of the day the book of the i-th child is returned back to him for the first time in this query.

Example

Input


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


Output


1 1 1 1 1 
3 3 3 
2 3 3 2 1 3 
1 
2 2 2 2 
4 4 4 1 4 

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;

import static java.lang.Math.*;

import java.util.concurrent.ThreadLocalRandom;

public class Sol implements Runnable {

  long mod = (long) 1e9 + 7;

  void solve(InputReader in, PrintWriter w) {
    int q = in.nextInt();
    while(q-- > 0) {
      int n = in.nextInt();
      int[] p = new int[n + 1];
      int[] result = new int[n + 1];
      for(int i = 1; i <= n; i++) p[i] = in.nextInt();
      for(int i = 1; i <= n; i++) {
        if(result[i] == 0) {
          int ind = i;
          int res = 1;
          while(p[ind] != i) {
            ind = p[ind];
            res++;
          }
          ind = i;
          while(p[ind] != i) {
            result[ind] = res;
            ind = p[ind];
          }
          result[ind] = res;
        }
      }
      for(int i = 1; i <= n; i++) w.print(result[i] + " ");
      w.println();
    }
  }

  // ************* Code ends here ***************

  void init() throws Exception {
    //Scanner in;
    InputReader in;
    PrintWriter w;
    boolean online = false;

    String common_in_fileName = "\\Samplein";
    String common_out_fileName = "\\in";
    int test_files = 0;

    for (int file_no = 0; file_no <= test_files; file_no++) {

      String x = "" + file_no;
      if (x.length() == 1) x = "0" + x;

      String in_fileName = common_in_fileName;// + "" + x;
      String out_fileName = common_out_fileName + "" + x;

      if (online) {
        //in = new Scanner(new File(in_fileName + ".txt"));
        in = new InputReader(new FileInputStream(new File(in_fileName + ".txt")));
        w = new PrintWriter(new FileWriter(out_fileName + ".txt"));
      } else {
        //in = new Scanner(System.in);
        in = new InputReader(System.in);
        w = new PrintWriter(System.out);
      }

      solve(in, w);
      w.close();
    }
  }

  public void run() {
    try {
      init();
    } catch (Exception e) {
      System.out.println(e);
      e.printStackTrace();
    }
  }

  static class InputReader {

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

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

    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 String nextLine() {
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }

    public int nextInt() {
      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 nextLong() {
      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 double nextDouble() {
      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, nextInt());
        }
        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, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

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

    public interface SpaceCharFilter {

      public boolean isSpaceChar(int ch);
    }
  };

  public static void main(String args[]) throws Exception {
    new Thread(null, new Sol(), "Sol", 1 << 28).start();
  }
}