Problem Statement

Given an integer array ARR of size N, replace each element of this array with its corresponding rank.

Explanation

The rank of an element is an integer between 1 and N (inclusive) that represents its size relative to other elements in the array. Here are the rules to determine the rank:

1. Ranks start from 1.
2. Larger elements receive larger ranks. Equal elements share the same rank.
3. Ranks should be assigned as small as possible.

Input

The first line contains an integer T, the number of test cases.
Following is 2*T lines describing the test cases:
For each test case, the first line contains an integer N (the number of elements in ARR).
The second line contains N space-separated integers, the elements of ARR.

Output

For each test case, print the elements of ARR separated by spaces, with each element replaced by its rank.

Example

Input:

2
5
50 30 20 40 10
3
100 200 100

Output:

5 3 2 4 1
2 3 2

Constraints

• 1 <= T <= 50
• 1 <= N <= 10^4
• -10^9 <= ARR[i] <= 10^9
• The array ARR[i] denotes the ith element of the array.

Note

You do not need to print anything; instead, return the integer array ARR with each element replaced by its rank.