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.Vector;
import java.util.*;
import java.lang.Math;
import java.util.concurrent.TimeUnit;
import java.util.stream.Collectors;
import javax.management.Query;
import java.io.*;
import java.math.BigInteger;

public class Main {
    static int mod = 1000000007;

    /* ======================DSU===================== */
    static class dsu {
        static int parent[], n;// min[],value[];
        static long rank[];
        dsu(int n) {
            parent = new int[n + 1];
            rank = new long[n + 1];
            // min=new int[n+1];
            // value=new int[n+1];
            this.n = n;
            makeSet();
        }

        static void makeSet() {
            for (int i = 1; i <= n; i++) {
                parent[i] = i;
                rank[i] = 1;
                // min[i]=i;
            }
        }

        static int find(int a) {
            if (parent[a] == a)
                return a;
            else {
                return parent[a] = find(parent[a]);// Path Compression
            }
        }

        static void union(int a, int b) {
            int setA = find(a);
            int setB = find(b);
            if (setA == setB)
                return;
            if (rank[setA] >= rank[setB]) {
                parent[setB] = setA;
                rank[setA]+=rank[setB];
                // if (rank[setA] == rank[setB]) {
                //     rank[setA]++;
                //     // rank[setB] = 0;
                // }
            } else {
                parent[setA] = setB;
                // rank[setA] = 0;
                rank[setB]+=rank[setA];
            }
        }
    }

    /* ======================================================== */
    static class Pair implements Comparator<Pair> {
        long x;
        long y;

        // Constructor
        public Pair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public Pair() {
        }

        @Override
        public int compare(Main.Pair o1, Main.Pair o2) {
            if (o1.y < o2.y)
                return -1;
            if (o1.y > o2.y)
                return 1;
            if (o1.y == o2.y) {
                if (o1.x <= o2.x) {
                    return -1;
                } else {
                    return 1;
                }
            }
            return 0;
        }
    }

    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;
        }

        int[] intArr(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] longArr(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

    static FastReader f = new FastReader();
    static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (long i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static int LowerBound(int a[], int x) { // smallest index having value >= x
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    static int UpperBound(int a[], int x) {// biggest index having value <= x
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] <= x)
                l = m;
            else
                r = m;
        }
        return l + 1;
    }

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

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long power(long x, long y, long p) {
        long res = 1;
        x = x % p;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }
        return res;
    }

    static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x);
            y >>= 1;
            x = (x * x);
        }
        return res;
    }

    static int power(int x, int y) {
        int res = 1;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x);
            y >>= 1;
            x = (x * x);
        }
        return res;
    }

    static int ceil(int x, int y) {
        return (x % y == 0 ? x / y : (x / y + 1));
    }

    static long ceil(long x, long y) {
        return (x % y == 0 ? x / y : (x / y + 1));
    }

    /*
     * ===========Modular Operations==================
     */
    static long modInverse(long n, long p) {
        return power(n, p - 2, p);
    }

    static long modAdd(long a, long b) {
        return (a % mod + b % mod) % mod;

    }

    static long modMul(long a, long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    static long nCrModPFermat(int n, int r) {
        long p = 1000000007;
        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;
    }

    /*
     * ===============================================
     */
    List<Integer> removeDup(ArrayList<Integer> list) {
        List<Integer> newList = list.stream().distinct().collect(Collectors.toList());
        return newList;
    }

    static void ruffleSort(long[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            long temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            int temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    /*
     * ===========Dynamic prog Recur Section===========
     */

    static int DP[][];
    static ArrayList<ArrayList<Integer>> g;
    static int count = 0;

    static ArrayList<Long> bitMask(ArrayList<Long> ar, int n) {
        ArrayList<Long> ans = new ArrayList<>();
        for (int mask = 0; mask <= Math.pow(2, n) - 1; mask++) {
            long sum = 0;
            for (int i = 0; i < n; i++) {
                if (((1 << i) & mask) > 0) {
                    sum += ar.get(i);
                }
            }
            ans.add(sum);
        }
        return ans;
    }

    /*
     * ====================================Main=================================
     */
    public static void main(String args[]) throws Exception {

        // File file = new File("D:\\VS Code\\Java\\Output.txt");
        // FileWriter fw = new FileWriter("D:\\VS Code\\Java\\Output.txt");
        Random rand = new Random();
        int t = 1;
        t = f.nextInt();
        while (t-- != 0) {
            int n = f.nextInt();
            dsu ob=new dsu(n);
            int a[] = new int[n+1];
            for (int i = 1; i <=n; i++) {
                a[i] = f.nextInt();
                // ob.parent[i]=a[i];
            }
            for(int i=1;i<=n;i++){
                ob.union(i, a[i]);
            }
            // for(int i=1 ;i<=n;i++){
            //     w.write(ob.parent[i]+" ");
            // }
            // w.write("\n");
            for(int i=1;i<=n;i++){
                w.write((ob.rank[ob.find(a[i])])+" ");
            }
            w.write("\n");
        }
        w.flush();
    }
}