Problem A

(Program filename: A.CPP or A.PAS or A.DPR or A.java)

Parencodings

Let *S* = *s*_{1} *s*_{2} … *s*_{2n }be a well-formed string of parentheses. S can be encoded in two different ways:

- By an integer sequence
*P*=*p*_{1}*p*_{2}…*p*where_{n}*p*is the number of left parentheses before the_{i}*i*th right parenthesis in*S*(*P*-sequence). - By an integer sequence
*W*=*w*_{1}*w*_{2}…*w*where for each right parenthesis, say_{n }*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 (filename: A.IN)

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.

Output (filename: A.OUT)

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

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