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Language:
Binary codes
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 6532Accepted: 2596

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.

b1b2…bN−1bN
b2b3…bNb1
…
bN−1bN…bN−3bN−2
bNb1…bN−2bN−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

00011
00110
01100
10001
11000

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)

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