B :: Parencodings

Time Limit: 2 Seconds    Memory Limit: 32768 KB

Let S = s1 s2 … s2n  be a well-formed string of parentheses. S can be encoded in two different ways:

  • By an integer sequence P = p1 p2 … pn where pi is the number of left parentheses before the ith right parenthesis in S (P-sequence).

  • By an integer sequence W = w1 w2 … wn where for each right parenthesis, say a in S, we associate an integer which is the number of right parentheses counting from the matched left parenthesis of a up to a. (W-sequence).

 

Following is an example of the above encodings:

 

	S		(((()()())))
	P-sequence	    4 5 6666
	W-sequence	    1 1 1456

 

Write a program to convert P-sequence of a well-formed string to the W-sequence of the same string.

Input

The first line of the input file contains a single integer t (1 <= t <= 100), the number of test cases, followed by the input data for each test case. The first line of each test case is an integer n (1 <= n <= 20), and the second line is the P-sequence of a well-formed string. It contains n positive integers, separated with blanks, representing the P-sequence.

Output

The output file consists of exactly t lines corresponding to test cases. For each test case, the output line should contain n integers describing the W-sequence of the string corresponding to its given P-sequence.

Sample Input

3
3
1 2 3
6
4 5 6 6 6 6
9 
4 6 6 6 6 8 9 9 9

Sample Output

1 1 1
1 1 1 4 5 6
1 1 2 4 5 1 1 3 9
Submit

Source: 12th Iran Nationwide Internet Contest I