Permutation Transformation

题意翻译

给您一个**排列** $a$ ，要求建一颗树，方式如下： - 选择当前排列中的**最大数**作为根的编号。 - 最大数左边的所有数按上述方法建左子树，如果左边没有数，则该结点没有左儿子。 - 最大数右边的所有数按上述方法建右子树，如果右边没有数，则该结点没有右儿子。 请您求出按上述方式建立的树的每个结点的深度，根节点深度为 $0$ 。 共有 $T(1\leq T\leq 100)$ 组数据，每组数据给出 $n(1\leq n\leq 100)$ 和排列 $a_1,a_2,\dots,a_n$。 对于每组数据，按**结点编号顺序**输出每个结点在树上的深度。

题目描述

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 \dots 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 \dots 1] = [3] $ , and the right one — for the subarray $ a[3 \dots 5] = [2, 1, 4] $ . As a result, the following tree will be built: 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: 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 $ .

输入输出格式

输入格式

The first line contains one integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Then $ t $ test cases follow. The first line of each test case contains an integer $ n $ ( $ 1 \le n \le 100 $ ) — the length of the permutation. This is followed by $ n $ numbers $ a_1, a_2, \ldots, a_n $ — permutation $ a $ .

输出格式

For each test case, output $ n $ values — $ d_1, d_2, \ldots, d_n $ .

输入输出样例

输入样例 #1

3
5
3 5 2 1 4
1
1
4
4 3 1 2

输出样例 #1

1 0 2 3 1 
0 
0 1 3 2