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.util.*;
import java.io.*;
 
public class AiseHi {
	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; 
        } 
    }
	public static void main (String[] args) {
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = 1;
    	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();
    		 Map<Integer,Integer> hm = new HashMap<>();
    		 for(int i=0;i<n;i++) {
    			 hm.put(a[i], i);
    		 }
    		 int res[] = new int[n];
    		 Queue<pair> q = new LinkedList<>();
    		 q.add(new pair(0,n-1,n,0));
    		 while(!q.isEmpty()) {
    			 pair p = q.poll();
    			 int b1 = p.a;
    			 int b2 = p.b;
    			 int val = p.val;
    			 int d = p.d;
    			 int idx = hm.get(val);
    			 res[idx] = d;
    			 if(b1 == b2) continue;
    			 int max = 0;
    			 for(int i=b1;i<idx;i++)
    				 max = Math.max(max, a[i]);
    			 if(max!=0)
    			 q.add(new pair(b1,idx-1,max,d+1));
    			 max = 0;
    			 for(int i=idx+1;i<=b2;i++)
    				 max = Math.max(max, a[i]);
    			 if(max!=0)
    			 q.add(new pair(idx+1,b2,max,d+1));
    		 }
    		 for(int i=0;i<n;i++)
    			 out.write(res[i]+" ");
    		 out.write("\n");
    	}
		out.close();
	}
	
	private static long pow(int i, int x) {
		long ans = 1;
		while(x>0) {
			if(x%2==0) {
				i*=i;
				x/=2;
			}
			else {
				ans*=i;
				x--;
			}
		}
//		System.out.println(ans+" ans");
		return ans;
	}

	static long findl(long[] a, int l, int h, long val, long k) {
		int ans = -1;
		while(l<=h) {
			int mid = (l+h)/2;
			if(a[mid] - val<=k) {
				ans = mid;
				l = mid + 1;
			}
			else h = mid-1;
		}
		return ans==-1?0:ans;
	}
	static long findh(long[] a, int l, int h, long val, long k) {
		int ans = -1;
		while(l<=h) {
			int mid = (l+h)/2;
			if(val - a[mid]<=k) {
				ans = mid;
				h = mid - 1;
			}
			else l = mid+1;
		}
		return ans==-1?0:ans;
	}
	
	private static int ub(List<Long> list, long l) {
		int lo = 0,h = list.size()-1;
		int ans = -1;
		while(lo<=h) {
			int mid = lo+(h-lo)/2;
			if(list.get(mid)<=l) {
				lo = mid+1;
				ans = mid;
			}
			else {
				
				h = mid-1;
			}
		}
		
		return ans+1;
	}
	private static long lb(List<Long> list, long l) {
		int lo = 0,h = list.size()-1;
		int ans = -1;
		while(lo<=h) {
			int mid = lo+(h-lo)/2;
			if(list.get(mid)<=l) {
				if(mid>0 && list.get(mid-1)==l) h = mid - 1;
				else {
					lo = mid+1;
					ans = mid;
				}
			}
			else {
				h = mid-1;
			}
		}
		if(list.get(ans)==l) return ans;
		return ans+1;
	}
	private static void swap(int[] a, int i, int j) {
		int temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	static long lstbt(long val) {
		long msk = val & (val-1);
		return (long) (Math.log(val^msk)/Math.log(2));
	}
	private static long sqrt(long x) {
		long l = 1,h = x;
		long ans = 0;
		while(l<=h) {
			long mid = (l+(h-l)/2);
			if(mid>x/mid) h = mid-1;
			else {
				ans = mid;
				l = mid+1;
			}
		}
		return ans;
	}
	static boolean prime[] = new boolean[10000001];
	static void sieve() {
		prime[0] = true;
		prime[1] = true;
		int max = 10000000;
		for(int i=2;i*i<=max;i++) {
			if(!prime[i]) {
				for(int j=i*i;j<=max;j+=i)
					prime[j] = true;
			}
		}
	}
	static String reverse(String x) {
		StringBuilder input1 = new StringBuilder();
		
        input1.append(x);
        
        input1 = input1.reverse();
        
        return input1.toString();
	}
	static int gcd(int val, int g) {
 
		if(g==0) return val;
		
		return gcd(g,val%g);
	}
	static int lcm(int a,int b) {
		return (a*b)/gcd(a,b);
	}
}
class pair implements Comparable<pair>{
	int a;
	int b;
	int val;
	int d;
	pair(int a,int b,int val,int d){
		this.a = a;
		this.b = b;
		this.val = val;
		this.d = d;
	}
	@Override
	public int compareTo(pair o) {
		return (int) (this.a - o.a);
	}
}