# Parencodings

Time Limit: 2 Seconds Memory Limit: 32768 KB

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

The first line of the input file contains a single integer *t* (1 <= *t* <= 100), 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 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

3 3 1 2 3 6 4 5 6 6 6 6 9 4 6 6 6 6 8 9 9 9

## Sample Output

1 1 1 1 1 1 4 5 6 1 1 2 4 5 1 1 3 9Submit

Source: 12th Iran Nationwide Internet Contest I