Magic Bitstrings
Description:
A bitstring, whose length is one less than a prime, might be magic. 1001 is one such string. In order to see the magic in the string let us append a non-bit x to it, regard the new thingy as a cyclic string, and make this square matrix of bits
| each bit | 1001 |
| every 2nd bit | 0110 |
| every 3rd bit | 0110 |
| every 4th bit | 1001 |
This matrix has the same number of rows as the length of the original bitstring. The m-th row of the matrix has every m-th bit of the original string starting with the m-th bit. Because the enlarged thingy has prime length, the appended x never gets used.
If each row of the matrix is either the original bitstring or its complement, the original bitstring is magic.
Input:
Each line of input (except last) contains a prime number p <= 100000. The last line contains 0 and this line should not be processed.
Output:
For each prime number from the input produce one line of output containing the lexicographically smallest, non-constant magic bitstring of length p-1, if such a string exists, otherwise output Impossible.
Sample Input:
5 3 17 47 2 79 0
Sample Output:
0110 01 0010111001110100 0000100001101010001101100100111010100111101111 Impossible 001001100001011010000001001111001110101010100011000011011111101001011110011011
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