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ZOJ Problem Set - 2481
Unique Ascending Array

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Given an array of integers A[N], you are asked to decide the shortest array of integers B[M], such that the following two conditions hold.

  • For all integers 0 <= i < N, there exists an integer 0 <= j < M, such that A[i] == B[j]
  • For all integers 0 =< i < j < M, we have B[i] < B[j]

Notice that for each array A[] a unique array B[] exists.


Input

The input consists of several test cases. For each test case, an integer N (1 <= N <= 100) is given, followed by N integers A[0], A[1], ..., A[N - 1] in a line. A line containing only a zero indicates the end of input.


Output

For each test case in the input, output the array B in one line. There should be exactly one space between the numbers, and there should be no initial or trailing spaces.


Sample Input

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


Sample Output

1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3



Author: SHI, Xiaohan
Source: Zhejiang Provincial Programming Contest 2005
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