2461：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 <= 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.