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 Main {
    InputReader in;
    Helper_class h;
    final long mod=1000000007;
    public static void main(String[] args) throws java.lang.Exception {
        new Main().run();
    }
    void run() throws Exception {
        in=new InputReader(System.in);
        StringBuilder sb = new  StringBuilder(); 
        h = new Helper_class();       
        int t=h.i();
        for(int i=1;i<=t;i++)
            solve(sb);
        System.out.print(sb);
    }
    int a[], d[], k=0;
    void cal(int l, int r, int k) {
        if(l>r)
            return;
        if(l==r) {
            d[l]=k;
            return;
        }
        int max=0, pos=-1;
        for(int i=l;i<=r;i++) {
            if(a[i]>max) {
                max=a[i];
                pos=i;
            }
        }
        d[pos]=k;
        cal(l, pos-1, k+1);
        cal(pos+1, r, k+1);
    }
    void solve(StringBuilder sb) {
        int i, j;
        int n=h.i(), cnt=0;
        k=0;
        a=new int[n];
        d=new int[n];
        for(i=0;i<n;i++)
            a[i]=h.i();
        int l=0, r=n-1;   
        cal(l, r, 0);
        for(i=0;i<n;i++)
            sb.append(d[i]+" ");
        sb.append("\n");
    }
    class Helper_class{
        long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
        int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
        String s(){return in.next();}
        int i(){return Integer.parseInt(in.next());}
        long l(){return Long.parseLong(in.next());}
        double d(){return Double.parseDouble(in.next());}
        long square(int x) {return ((long)x * (long)x);}
        long mul(long x, long y) {long ans = x*y;return (ans>=mod ? ans%mod : ans);}
        long power(long x, long y, long p) {  
            long res = 1;       
            x = x % p;  
            if (x == 0) return 0;   
            while (y > 0) {
                if((y & 1)==1) 
                    res = (res * x) % p;  
                y = y >> 1;  
                x = (x * x) % p;  
            } 
            return res%p; 
        } 
        void sorter(int a[]) {
            ArrayList<Integer> ar=new ArrayList<>();
            for(int i=0;i<a.length;i++)
                ar.add(a[i]);
            Collections.sort(ar);
            for(int i=0;i<ar.size();i++)
                a[i]=ar.get(i);
        }
        int lower(int a[], int k) {
            int l=0, r=a.length-1, ans=-1;
            while(l<=r) {
                int mid = (r+l)/2;
                if(a[mid]>k)
                    r=mid-1;
                else {
                    ans=mid;
                    l=mid+1;
                }
            }
            if(ans!=-1)
                ans=a[ans];
            return ans;
        }
        int upper(int a[], int k) {
            int l=0, r=a.length-1, ans=-1;
            while(l<=r) {
                int mid = (r+l)/2;
                if(a[mid]<k)
                    l=mid+1;
                else {
                    ans=mid;
                    r=mid-1;
                }
            }
            if(ans!=-1)
                ans=a[ans];
            return ans;
        }
        void reverse(int a[]) {
            for(int i=0;i<a.length/2;i++) {
                int x=a[i];
                a[i]=a[a.length-1-i];
                a[a.length-1-i]=x;
            }
        }
        //String.format("%.kf",x)
    }
    class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
        public void skip(int x) {
            while (x-->0)
                read();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public String nextString() {
            return next();
        }
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
        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 boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}