# Inversion

Time Limit: 1 Second Memory Limit: 32768 KB

Let { A1,A2,...,An } be a permutation of the set{ 1,2,..., n}. If i < j and Ai > Aj then the pair (Ai,Aj) is called an "inversion" of the permutation. For example, the permutation {3, 1, 4, 2} has three inversions: (3,1), (3,2) and (4,2).The inversion table B1,B2,...,Bn of the permutation { A1,A2,...,An } is obtained by letting Bj be the number of elements to the left of j that are greater than j. (In other words, Bj is the number of inversions whose second component is j.) For example, the permutation:

{ 5,9,1,8,2,6,4,7,3 }

has the inversion table

2 3 6 4 0 2 2 1 0

since there are 2 numbers, 5 and 9, to the left of 1; 3 numbers, 5, 9 and 8, to the left of 2; etc.

Perhaps the most important fact about inversions is Marshall Hall's observation that an inversion table uniquely determines the corresponding permutation. So your task is to convert a permutation to its inversion table, or vise versa, to convert from an inversion table to the corresponding permutation.

## Input

The input consists of several test cases. Each test case contains two lines.The first line contains a single integer N ( 1 <= N <= 50) which indicates the number of elements in the permutation/invertion table.

The second line begins with a single charactor either 'P', meaning that the next N integers form a permutation, or 'I', meaning that the next N integers form an inversion table.

Following are N integers, separated by spaces. The input is terminated by a line contains N=0.

## Output

For each case of the input output a line of intergers, seperated by a single space (no space at the end of the line). If the input is a permutation, your output will be the corresponding inversion table; if the input is an inversion table, your output will be the corresponding permutation.## Sample Input

9 P 5 9 1 8 2 6 4 7 3 9 I 2 3 6 4 0 2 2 1 0 0

## Sample Output

2 3 6 4 0 2 2 1 0 5 9 1 8 2 6 4 7 3Submit

Source: Zhejiang University Local Contest 2002, Preliminary