# Magic Bitstrings

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.

Each line of input (except last) contains a prime number
$p \leq 100000$. The last
line contains 0 and this line should not be processed. 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 1 | Sample Output 1 |
---|---|

5 3 17 47 2 79 0 |
0110 01 0010111001110100 0000100001101010001101100100111010100111101111 Impossible 001001100001011010000001001111001110101010100011000011011111101001011110011011 |