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.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.* ;
import java.io.* ;
@SuppressWarnings("unused")

//Scanner s = new Scanner(new File("input.txt"));
//s.close();
//PrintWriter writer = new PrintWriter("output.txt");
//writer.close();
//BufferedReader in = new BufferedReader(new InputStreamReader(System.in)) ;

//Scanner in = new Scanner(System.in) ;
//[a-z] = [97-122] ------- [A-Z] = [65-90]

public class cf
{	
	static final int mod = 1000000007 ;
	
	static boolean not_prime[] = new boolean[1000001] ;
	static void sieve() {
		for(int i=2 ; i*i<1000001 ; i++) {
			if(not_prime[i]==false) {
				for(int j=2*i ; j<1000001 ; j+=i) {
					not_prime[j]=true ;
				}
			}
		}not_prime[0]=true ; not_prime[1]=true ;
	}	
	
	public static long bexp(long base , long power)
	{
		long res=1L ;
		
		//base = base%mod ;
		
		while(power>0) {
			if((power&1)==1) {
				res=(res*base);//%mod ;
				power-- ;
			}
			else {
				base=(base*base);//%mod ;
				power>>=1 ;
			}
		}
		
		return res ;
	}

	static long modInverse(long n, long p)
	{
	    return power(n, p - 2, p);
	}
	static long power(long x, long y, long p)
	{
	  
	    // Initialize result
	    long res = 1;
	  
	    // Update x if it is more than or
	    // equal to p
	    x = x % p;
	  
	    while (y > 0) {
	  
	        // If y is odd, multiply x
	        // with result
	        if (y % 2 == 1)
	            res = (res * x) % p;
	  
	        // y must be even now
	        y = y >> 1; // y = y/2
	        x = (x * x) % p;
	    }
	  
	    return res;
	}
	static long nCrModPFermat(int n, int r, long p)
	{
		if(n<r) return 0 ;
	    if (r == 0)
	        return 1;

	    long[] fac = new long[n + 1];
	    fac[0] = 1;
	  
	    for (int i = 1; i <= n; i++)
	        fac[i] = fac[i - 1] * i % p;
	  
	    return (fac[n] * modInverse(fac[r], p) % p
	            * modInverse(fac[n - r], p) % p)
	        % p;
	}
	
	private static long modular_add(long a, long b)
	{
	    return ((a % mod) + (b % mod)) % mod;
	}
	private static long modular_sub(long a, long b)
	{
	    return ((a % mod) - (b % mod) + mod) % mod;
	}
	private static long modular_mult(long a, long b)
	{
	    return ((a % mod) * (b % mod)) % mod;
	}
	
	static long lcm(int a, int b)
	{
		return (a / gcd(a, b)) * b;
	}
	private static long gcd(long a, long b)
	{
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble(){ return Double.parseDouble(next()); };
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
	
	static HashMap<Integer , ArrayList<Integer>> map = new HashMap<>() ;
	static boolean vis[] ;

	public static void main(String[] args)throws IOException//throws FileNotFoundException
    {
    	FastReader in = new FastReader() ;	
		StringBuilder op = new StringBuilder() ;

		int t = in.nextInt() ;
		while(t-->0)
		{
			int n = in.nextInt() ;
			int dis[] = new int[n+1] ;
			int a[] = new int[n+1] ;
			for(int i=1 ; i<n+1 ; i++)
				a[i] = in.nextInt() ;
			int curr=1 ;
			vis = new boolean[n+1] ;
			for(int i=1 ; i<n+1 ; i++)
			{
				List<Integer> li = new ArrayList<>() ;
				int el = i ;
				if(!vis[el]) {
					while(!vis[el]) {
						li.add(el) ;
						vis[el]=true ;
						el=a[el] ;
					}
				}
				for(int i1=0 ; i1<li.size() ; i1++)dis[li.get(i1)]=li.size() ;
			}
			for(int i=1 ; i<n+1 ; i++)System.out.print(dis[i]+" ");
			System.out.println();
		}
    }
}