Parencodings

Time Limit: 2 Seconds
Memory Limit: 65536 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 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.

**Output**

The output 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**

2

6

4 5 6 6 6 6

9

4 6 6 6 6 8 9 9 9

**Sample Output**

1 1 1 4 5 6

1 1 2 4 5 1 1 3 9

Source:

**Asia 2001, Tehran (Iran)**
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