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.awt.*;
import java.io.*;
import java.util.*;
import java.util.List;

public class Hell {
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        int t=sc.nextInt();
        while (t-->0){
            int n=sc.nextInt();
            int a[]=new int[n];
            for (int i=0;i<n;i++){
                a[i]=sc.nextInt()-1;
            }
            int mx[][]=new int[n][n];
            for (int i=0;i<n;i++){
                for (int j=i;j<n;j++){
                    if (j==i)mx[i][j]=i;
                    else if (a[mx[i][j-1]]>a[j]){
                        mx[i][j]=mx[i][j-1];
                    }else mx[i][j]=j;
                }
            }
//            for (int i=0;i<n;i++){
//                for (int j=i;j<n;j++){
//                    System.out.println(i+" "+j+" "+mx[i][j]);
//                }
//            }

            TreeNode root=new TreeNode();
            solve(0, n-1, root, mx, a);
            int ans[]=new int[n];
            traverse(root, root, ans,a);
            StringBuilder sb=new StringBuilder();
            for (int x:a){
                sb.append((ans[x]-1)+" ");
            }
            System.out.println(sb);

        }
    }

    static void traverse(TreeNode root, TreeNode prev, int ans[], int a[]){
//        System.out.println(root.val+" "+prev.val);
        ans[a[root.val]]=ans[a[prev.val]]+1;
        if (root.l!=null)traverse(root.l, root, ans,a);
        if (root.r!=null)traverse(root.r, root, ans,a);
    }

    static TreeNode solve(int l,int r, TreeNode cur, int mx[][], int a[]){
        if(l>r)return null;
        int max=mx[l][r];
        if (cur==null)cur=new TreeNode();
        cur.val=max;
        cur.l=solve(l, max-1, cur.l, mx, a);
        cur.r=solve(max+1, r, cur.r, mx, a);
        return cur;
    }

    static class TreeNode{
        TreeNode l,r;
        int val;
        public TreeNode(int val){
            this.val=val;
        }
        public TreeNode(){

        }
    }

    public static long maximumArea(int arr[]){
        int n=arr.length;
        long suf[]=new long[n];
        suf[n-1]=arr[n-1];
        for (int i=n-2;i>=0;i--){
            suf[i]=arr[i]*(n-i);
        }
        for(int i=n-2;i>=0;i--){
            suf[i]=Math.max(suf[i], suf[i+1]);
        }
        long ans=0;
        for (int i=0;i<n-1;i++){
            ans=Math.max((long) arr[i]*(i+1)+suf[i+1], ans);
        }
        return ans;
    }

    public static int[] itemsCollected(int t[]){
        int n = t.length;
        int i=0, j=n-1;
        long sumi=0, sumj=0;
        while (i<=j){
            while (i<=j && sumi<=sumj){
                sumi+=t[i];
                i++;
            }
            while (i<=j && sumi>sumj){
                sumj+=t[j];
                j--;
            }
        }
        return new int[]{i, n-j-1};
    }

    public static long minimumCost(int c[], int q[]){
        PriorityQueue<Point> pq=new PriorityQueue<Point>(new Comparator<Point>() {
            @Override
            public int compare(Point o1, Point o2) {
                return o1.c-o2.c;
            }
        });
        int n=c.length;
        long ans=0;
        for (int i=0;i<n;i++){
            pq.add(new Point(c[i], q[i]));
            Point pop=pq.poll();
            ans+=pop.c;
            if (pop.q-1==0)continue;
            pq.add(new Point(pop.c, pop.q-1));
        }
        return ans;
    }
    static class Point{
        int c, q;
        Point(int c, int q){
            this.c=c;
            this.q=q;
        }
    }

    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;
        }
    }
}