Binary codes   poj1147
Time Limit:1000MS Memory Limit:65536K
Total Submit:1695 Accepted:626

Description

Consider a binary string (b1…bN) with N binary digits. Given such a string, the matrix of Figure 1 is formed from the rotated versions of the string.

  b1   b2 … bN-1 bN

  b2   b3 … bN   b1

  …

  bN-1 bN … bN-3 bN-2

  bN   b1 … bN-2 bN-1



  Figure 1. The rotated matrix

Then rows of the matrix are sorted in alphabetical order, where ‘0’ is before ‘1’. You are to write a program which, given the last column of the sorted matrix, finds the first row of the sorted matrix.

As an example, consider the string (00110). The sorted matrix is

  0 0 0 1 1

  0 0 1 1 0

  0 1 1 0 0

  1 0 0 0 1

  1 1 0 0 0

and the corresponding last column is (1 0 0 1 0). Given this last column your program should determine the first row, which is (0 0 0 1 1).

Input

The first line contains one integer N ≤ 3000, the number of binary digits in the binary string. The second line contains N integers, the binary digits in the last column from top to bottom.

Output

The first line contains N integers: the binary digits in the first row from left to right.

Sample Input

5
1 0 0 1 0

Sample Output

0 0 0 1 1

Source
IOI 2001 (back-up task)


[ 此贴被kangtalc在2007-04-16 12:28重新编辑 ]

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