Parencodings
Program |
PARENC.C, PARENC.CPP, PARENC.PAS |
Let S = s1 s2 … s2n be a well-formed string of parentheses. S can be
encoded in two different ways:
- q 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).
- q 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