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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.HashMap;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	private BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	private StringTokenizer st;
	private Long MOD = 1000000007L;
	private final String endl = "\n";

	public static void main(String[] args) throws Exception {
		new Main().solve();
	}

	private void solve() throws Exception {

		int testCases = 1;
		testCases = Integer.parseInt(in.readLine().trim());
		preProcess();
		for (int i = 1; i <= testCases; i++) {
			solveTestCase(i);
		}

		out.flush();
		out.close();
	}

	void preProcess() {
		
	}

	private void solveTestCase(int testCaseNumber) throws Exception {
		int n = ri();
		int arr[] = ria(n);
		
		int ans[] = new int[n];
		
		solve(0, n-1, arr, ans, 0);
		
		for (int x : ans) {
			out.write(x + " ");
		}
		out.write(endl);
	}
	
	
	void solve(int a, int b, int[] arr, int[] ans, int level) {
		if ( b < a) return;
		int max = -1;
		int i = a;
		for (; i <= b; i++ ) {
			max = Math.max(max, arr[i]);
		}

		i = a;
		for (; i <= b; i++) {
			if (arr[i] == max) {
				break;
			}
		}
		
		ans[i] = level;
		
		solve(a, i - 1, arr, ans, level + 1);
		solve(i + 1, b, arr, ans, level + 1);
	}
	
	boolean[] sieveOfEratosthenes(int n) {
		// Create a boolean array "prime[0..n]" and initialize
		// all entries it as true. A value in prime[i] will
		// finally be false if i is Not a prime, else true.
		boolean prime[] = new boolean[n + 1];
		for (int i = 0; i < n; i++)
			prime[i] = true;

		for (int p = 2; p * p <= n; p++) {
			// If prime[p] is not changed, then it is a prime
			if (prime[p] == true) {
				// Update all multiples of p
				for (int i = p * p; i <= n; i += p)
					prime[i] = false;
			}
		}

		return prime;
	}

	// utils
	public long modInv(long a, long MOD) {
		return new BigInteger(a + "").modPow(new BigInteger((MOD - 2) + ""), new BigInteger(MOD + "")).longValue();
	}

	public long modPro(long a, long b, long MOD) {
		return ((a % MOD) * (b % MOD)) % MOD;
	}

	private long factorialMod(int n, long MOD) {
		long pro = 1;

		for (long i = 1; i <= n; i++) {
			pro = pro * i;
			pro %= MOD;
		}

		return pro;
	}

	// utilities below

	// IO UTILS

	void log(Object... args) {
		boolean testing = true;
		testing = false;

		if (!testing)
			return;

		for (Object s : args) {
			System.out.print(s.toString() + " ");
		}
		System.out.println();
	}

	String line() throws IOException {
		return in.readLine().trim();
	}

	StringTokenizer tokens() throws IOException {
		return new StringTokenizer(line());
	}

	long l(String s) {
		return Long.parseLong(s);
	}

	long rl() throws IOException {
		return l(line());
	}

	long[] rla(int n) throws IOException {
		long[] arr = new long[n];
		st = tokens();

		for (int i = 0; i < n; i++)
			arr[i] = l(st.nextToken());

		return arr;
	}

	int i(String s) {
		return Integer.parseInt(s);
	}

	int ri() throws IOException {
		return i(line());
	}

	int[] ria(int n) throws IOException {
		int[] arr = new int[n];
		st = tokens();

		for (int i = 0; i < n; i++)
			arr[i] = i(st.nextToken());

		return arr;
	}

	String rs() throws IOException {
		return line();
	}

	String[] rsa(int n) throws IOException {
		String s[] = new String[n];

		st = tokens();

		for (int i = 0; i < n; i++)
			s[i] = st.nextToken();

		return s;
	}

	double d(String s) {
		return Double.parseDouble(s);
	}

	double rd() throws IOException {
		return d(line());
	}

	double[] rda(int n) throws IOException {
		double[] arr = new double[n];
		st = tokens();

		for (int i = 0; i < n; i++) {
			arr[i] = d(st.nextToken());
		}

		return arr;
	}
	// IO UTILS END

	// MATH UTILS

	long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	// MATH UTILS END
}