21103_Parencodings

Let S = s₁s₂...s_2n be a well-formed string of parentheses. S can be encoded in two different ways:

• By an integer sequence P = p₁p₂...p_n where p_i is the number of left parentheses before the i-th right parenthesis in S (P-sequence).

• By an integer sequence W = w₁w₂...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:

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.

The first line of the input 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