Let S = s₁ s₂ … s_2n be a well-formed string of parentheses. S can be encoded in two different ways:

• By an integer sequence P = p₁ p₂ … p_n where p_i is the number of left parentheses before the ith right parenthesis in S (P-sequence).
• By an integer sequence W = w₁ w₂ … w_n 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:

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

The first line of the input file contains a single integer t (1 £ t £ 10), 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.

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.

2

6

4 5 6 6 6 6

9

4 6 6 6 6 8 9 9 9

1 1 1 4 5 6

1 1 2 4 5 1 1 3 9