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.lang.reflect.Type;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;
import java.util.concurrent.Future;
import java.util.concurrent.FutureTask;
import java.util.concurrent.locks.LockSupport;

public class Main {

    static class Task {

        public static String roundS(double result, int scale) {
            String fmt = String.format("%%.%df", scale);
            return String.format(fmt, result);
//        DecimalFormat df = new DecimalFormat("0.000000");
//        double result = Double.parseDouble(df.format(result));
        }

        int rt(int x) {
            if (x != fa[x]) {
                int to = rt(fa[x]);
                dp[x] ^= dp[fa[x]];
                fa[x] = to;
                return to;
            }
            return x;
        }

        void combine(int x, int y, int val) {
            int rt1 = rt(x);
            int rt2 = rt(y);

            if (rt1 == rt2) return;

            fa[rt1] = rt2;
            dp[rt1] = dp[x] ^ dp[y] ^ val;
            g--;

        }


        int fa[], dp[];
        int g;


        static int MAXN = 10000;
        static Random rd = new Random(348957438574659L);

        static int[] ch[],val,size,rnd,cnt;
        static int len=0,rt=0;

        // return new node, the node below s
        static int rotate(int s,int d){
            // child
            int x=ch[s][d^1];
            // give me grandson
            ch[s][d^1] = ch[x][d];
            // child become father
            ch[x][d]=s;
            // update size, update new son first
            update(s);
            update(x);
            return x;
        }

        static void update(int s){
            size[s] = size[ch[s][0]] + size[ch[s][1]] + cnt[s];
        }

        // 0 for left, 1 for right
        static int cmp(int x,int num) {
            if (val[x] == num) return -1;
            return num < val[x] ? 0 : 1;
        }

        static int insert(int s,int num) {
            if(s==0){
                s=++len;
                val[s]=num;size[s]=1;rnd[s]=rd.nextInt();cnt[s] = 1;
            }else{
                int d=cmp(s,num);
                if(d!=-1) {
                    ch[s][d]=insert(ch[s][d],num);
                    // father's random should be greater
                    if(rnd[s]<rnd[ch[s][d]]) {
                        s=rotate(s,d^1);
                    }else {
                        update(s);
                    }
                }else{
                    ++cnt[s];++size[s];
                }
            }
            return s;
        }

        static int del(int s,int num) {
            int d = cmp(s, num);
            if (d != -1) {
                ch[s][d] = del(ch[s][d], num);
                update(s);
            }else if (ch[s][0] * ch[s][1] == 0) {
                if(--cnt[s]==0){
                    s = ch[s][0] + ch[s][1];
                }
            } else {
                int k = rnd[ch[s][0]] < rnd[ch[s][1]] ? 0 : 1;
                // k points to smaller random value,then bigger one up
                s = rotate(s, k);
                // now the node with value num become the child
                ch[s][k] = del(ch[s][k], num);
                update(s);
            }
            return s;
        }

        static int getKth(int s, int k){
            int lz = size[ch[s][0]];
            if(k>=lz+1&&k<=lz+cnt[s]){
                return val[s];
            }else if(k<=lz){
                return getKth(ch[s][0], k);
            }else{
                return getKth(ch[s][1], k-lz-cnt[s]);
            }
        }

        static int getRank(int s,int value){
            if(s==0)return 1;
            if(value==val[s])return size[ch[s][0]] + 1;
            if(value<val[s])return getRank(ch[s][0],value);
            return getRank(ch[s][1],value)+size[ch[s][0]] + cnt[s];
        }


        static int getPre(int data){
            int ans= -1;
            int p=rt;
            while(p>0){
                if(data>val[p]){
                    if(ans==-1 || val[p]>val[ans])
                        ans=p;
                    p=ch[p][1];
                }
                else p=ch[p][0];
            }
            return ans!=-1?val[ans]:(-2147483647);
        }

        static int getNext(int data){
            int ans= -1;
            int p=rt;
            while(p>0){
                if(data<val[p]){
                    if(ans==-1 || val[p]<val[ans])
                        ans=p;
                    p=ch[p][0];
                }
                else p=ch[p][1];
            }

            return ans!=-1?val[ans]:2147483647;
        }


        static boolean find(int s,int num){
            while(s!=0){
                int d=cmp(s,num);
                if(d==-1) return true;
                else s=ch[s][d];
            }
            return false;
        }
        static int ans = -10000000;
        static boolean findX(int s,int num){
            while(s!=0){
                if(val[s]<=num){
                    ans = num;
                }
                int d=cmp(s,num);
                if(d==-1) return true;
                else {
                    s = ch[s][d];
                }
            }
            return false;
        }

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


        void linear_sort(int arr[]){
            int d =  65536;
            ArrayDeque bucket[] = new ArrayDeque[d];
            for(int j=0;j<d;++j){
                bucket[j] = new ArrayDeque();
            }
            for(int u:arr){
                bucket[u%d].offer(u);
            }
            int pos = 0;
            for(int j=0;j<d;++j){
                while(bucket[j].size()>0) {
                    arr[pos++] = (int)bucket[j].pollFirst();
                }
            }
            for(int u:arr){
                bucket[u/d].offer(u);
            }
            pos = 0;
            for(int j=0;j<d;++j){
                while(bucket[j].size()>0) {
                    arr[pos++] = (int)bucket[j].pollFirst();
                }
            }
        }

        public void dfs(int l,int r,int mx[][],int dep,int ans[]){
            if(l>r) return;
            int pos = mx[l][r];
            ans[pos] = dep;
            dfs(l,pos-1,mx,dep+1,ans);
            dfs(pos+1,r,mx,dep+1,ans);
        }


        public void solve(int testNumber, InputReader in, PrintWriter out) {

//            int a[] = {4,3,2,45,1,2,3,4,56,7,2,1,2};
//            linear_sort(a);
//            for(int u:a){
//                out.println(u);
//            }

            int t = in.nextInt();
//
//
            outer:for(int j=0;j<t;++j){
                int n = in.nextInt();
                int a[] = in.nextArray(n);

                int mx[][] = new int[n][n];

                for(int i=0;i<n;++i){
                    mx[i][i] = i;
                    for(int k=i+1;k<n;++k){
                        if(a[k]>a[mx[i][k-1]]){
                            mx[i][k] = k;
                        }else{
                            mx[i][k] = mx[i][k-1];
                        }
                    }
                }
                int r[] = new int[n];
                dfs(0,n-1,mx,0,r);
                for(int i=0;i<n;++i){
                    out.print(r[i]+" ");
                }
                out.println();




























            }






//            while(true) {
//                int n = in.nextInt();
//
//                int m  =in.nextInt();
//
//                fa = new int[n];
//                dp = new int[n];
//                for(int i=0;i<n;++i){
//                    fa[i] = i;
//                }
//                g =  n;
//                int c = 0;
//                int as[] = new int[n];
//                int bs[] = new int[n];
//                char xs[] = new char[n];
//
//                int at = -1;
//                Set<Integer> st = new HashSet<>();
//
//                for (int i = 0; i < n; ++i) {
//                    String line = in.next();
//                    int p = 0;
//                    int a = 0;
//                    while(Character.isDigit(line.charAt(p))){
//                        a =  a*10 + (line.charAt(p)-'0'); p++;
//                    }
//                    char x = line.charAt(p++);
//
//                    int b = 0;
//                    while(p<line.length()){
//                        b =  b*10 + (line.charAt(p)-'0'); p++;
//                    }
//
//                    as[i] = a;
//                    xs[i] = x;
//                    bs[i] = b;
//
//                    if(x=='='){
//                        int r1 = rt(a); int r2 = rt(b);
//                        if(r1==r2){
//                            if(dp[a]!=dp[b]){
//                                c++;
//                                at = i;
//                            }
//                        }else {
//                            combine(a, b, 0);
//                        }
//                    }else if(x=='<'){
//                        int r1 = rt(a); int r2 = rt(b);
//                        if(r1==r2){
//                            if(dp[a]>=dp[b]){
//                                c++;
//                                at = i;
//                            }
//                        }else {
//                            combine(a, b, -1);
//                        }
//                    }else{
//                        int r1 = rt(a); int r2 = rt(b);
//                        if(r1==r2){
//                            if(dp[a]<=dp[b]){
//                                c++;
//                                at = i;
//                            }
//                        }else {
//                            combine(a, b, 1);
//                        }
//                    }
//
//
//                }
//                if(g==1||c>=2){
//                    out.println("Impossible");
//                    continue;
//                }
//
//
//                for(int xuan: st){
//
//
//
//
//                }
//
//
//
//
//
//
//            }






        }


        static long mul(long a, long b, long p)
        {
            long res=0,base=a;
            while(b>0)
            {
                if((b&1L)>0)
                    res=(res+base)%p;
                base=(base+base)%p;
                b>>=1;
            }
            return res;
        }

        static long mod_pow(long k,long n,long p){
            long res = 1L;
            long temp = k%p;
            while(n!=0L){
                if((n&1L)==1L){
                    res = mul(res,temp,p);
                }
                temp = mul(temp,temp,p);
                n = n>>1L;
            }
            return res%p;
        }


        public static double roundD(double result, int scale){
            BigDecimal bg = new BigDecimal(result).setScale(scale, RoundingMode.UP);
            return bg.doubleValue();
        }



    }
    private static void solve() {
        InputStream inputStream = System.in;
//        InputStream inputStream  = null;
//        try {
//            inputStream = new FileInputStream(new File("D:\\chrome_download\\travel_restrictions_input.txt"));
//        } catch (FileNotFoundException e) {
//            e.printStackTrace();
//        }
        OutputStream outputStream = System.out;
//        OutputStream outputStream = null;
//        File f = new File("D:\\chrome_download\\travel_restrictions_output.txt");
//        try {
//            f.createNewFile();
//        } catch (IOException e) {
//            e.printStackTrace();
//        }
//        try {
//            outputStream = new FileOutputStream(f);
//        } catch (FileNotFoundException e) {
//            e.printStackTrace();
//        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task task = new Task();
        task.solve(1, in, out);
        out.close();
    }
    public static void main(String[] args) {
       // new Thread(null, () -> solve(), "1", (1 << 10 ) ).start();
        solve();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String nextLine() {
            String line = null;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public char nextChar() {
            return next().charAt(0);
        }
        public int[] nextArray(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; ++i) {
                res[i] = nextInt();
            }
            return res;
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}