Problem: A permutation — is a sequence of length n integers from 1 to n, in which all the numbers occur exactly once. For example, [1], [3, 5, 2, 1, 4], [1, 3, 2] — permutations, and [2, 3, 2], [4, 3, 1], [0] — no.

Polycarp was recently gifted a permutation a[1 ... n] of length n. Polycarp likes trees more than permutations, so he wants to transform permutation a into a rooted binary tree. He transforms an array of different integers into a tree as follows: 

  * the maximum element of the array becomes the root of the tree; 
  * all elements to the left of the maximum — form a left subtree (which is built according to the same rules but applied to the left part of the array), but if there are no elements to the left of the maximum, then the root has no left child; 
  * all elements to the right of the maximum — form a right subtree (which is built according to the same rules but applied to the right side of the array), but if there are no elements to the right of the maximum, then the root has no right child. 



For example, if he builds a tree by permutation a=[3, 5, 2, 1, 4], then the root will be the element a_2=5, and the left subtree will be the tree that will be built for the subarray a[1 ... 1] = [3], and the right one — for the subarray a[3 ... 5] = [2, 1, 4]. As a result, the following tree will be built: 

<image> The tree corresponding to the permutation a=[3, 5, 2, 1, 4].

Another example: let the permutation be a=[1, 3, 2, 7, 5, 6, 4]. In this case, the tree looks like this: 

<image> The tree corresponding to the permutation a=[1, 3, 2, 7, 5, 6, 4].

Let us denote by d_v the depth of the vertex a_v, that is, the number of edges on the path from the root to the vertex numbered a_v. Note that the root depth is zero. Given the permutation a, for each vertex, find the value of d_v.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 100) — the length of the permutation.

This is followed by n numbers a_1, a_2, …, a_n — permutation a.

Output

For each test case, output n values — d_1, d_2, …, d_n.

Example

Input


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


Output


1 0 2 3 1 
0 
0 1 3 2 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class TEST
{
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        public Reader() 
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public Reader(String file_name) throws IOException 
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public String nextString() throws IOException
        {
            String str00 = scan.next();
            return str00;
        }
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1)  
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
        String next() throws IOException 
        {
            int c;
            for (c = read(); c <= 32; c = read());
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = read())
            {
                sb.append((char) c);
            }
            return sb.toString();
        }
        public int nextInt() throws IOException 
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do 
            {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        } 
        public long nextLong() throws IOException 
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');           
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            } 
            if (neg)
                return -ret;
            return ret;
        }
        private void fillBuffer() throws IOException 
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
        private byte read() throws IOException 
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        } 
        public void close() throws IOException 
        {
            if (din == null)
                return;
            din.close();
        }
        public int[] nextArray(int n) throws IOException 
        {
            int[] a=new int[n];
            for (int i=0;i<n;i++)
            {
                a[i]=nextInt();
            }
            return a;
        }
        public long[] nextArrayl(int n) throws IOException 
        {
            long[] a = new long[n];
            for (int i=0;i<n;i++)
            {
                a[i]=nextLong();
            }
            return a;
        }
    }
    public static void sort(long a[])
    {
        int n=a.length;
        Long d[]=new Long[n];
        for(int i=0;i<n;i++)
        {
            d[i]=a[i];
        }
        Arrays.sort(d);
        for(int i=0;i<n;i++)
        {
            a[i]=d[i];
        }
    }
    public static void sort(int a[])
    {
        int n=a.length;
        Integer d[]=new Integer[n];
        for(int i=0;i<n;i++)
        {
            d[i]=a[i];
        }
        Arrays.sort(d);
        for(int i=0;i<n;i++)
        {
            a[i]=d[i];
        }
    }
    public static void fun(int a[],int ans[],int i,int j,int d)
    {
        if(i>j)
        {
            return;
        }
        int max=Integer.MIN_VALUE;
        int p=0;
        for(int in=i;in<=j;in++)
        {
            if(max<a[in])
            {
                max=a[in];
                p=in;
            }
        }
        ans[max]=d;
        fun(a,ans,i,p-1,d+1);
        fun(a,ans,p+1,j,d+1);
    }
    public static void main(String args[])throws IOException
    {
        Reader r=new Reader();
        int t=r.nextInt();
        while(t-->0)
        {
            int n=r.nextInt();
            int a[]=r.nextArray(n);
            int ans[]=new int[n+1];
            fun(a,ans,0,n-1,0);
            StringBuffer res=new StringBuffer();
            for(int i=0;i<n;i++)
            {
                res.append(ans[a[i]]+" ");
            }
            System.out.println(res);
        }
    }
}