Parencodings

Description

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 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

Source

Tehran 2001      

/*
POJ 1068 Parencodings
简单模拟
用数组a[i]表示第i个右括号和第i+1个右括号间的左括号数
然后逐渐找和右括号匹配的左括号所处的位置
i-j

*/


#include<stdio.h>
#include<iostream>

const int MAXN=50;
int P[MAXN];
int W[MAXN];
int a[MAXN];

int main()
{
    int T;
    int n;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        for(int i=1;i<=n;i++)
           scanf("%d",&P[i]);
        a[0]=P[1];
        for(int i=1;i<n;i++) a[i]=P[i+1]-P[i];
        int j;
        for(int i=1;i<=n;i++)
        {
            for(j=i-1;j>=0;j--)//匹配该右括号
            {
                if(a[j]>0)
                {
                    a[j]--;
                    break;
                }
            }
            W[i]=i-j;
        }
        for(int i=1;i<n;i++)printf("%d ",W[i]);
        printf("%d\n",W[n]);
    }
    return 0;
}