P8589 'JROI-8' Yes, There Are Also Flowers, Girls, and the Milky Way

 > "Part 1"\ Even if I turn into bones, there are still things I do not want to forget. **Reprint permission has been granted.**

Given $n$, construct a binary string of length $n$ containing only $0,1$ such that the numbers of occurrences of $01,00,10,11$ are equal, or report that there is no solution. Here, an "occurrence" means being exactly the same as a consecutive substring of the original string. For example, in $1011101$, the numbers of occurrences of $01,00,10,11$ are $2,0,2,2$, respectively. **Note that the large sample is not provided as an attached file, but is placed directly in Sample #3 of the Input/Output Samples.**

One line containing a positive integer $n$.

If there is a solution, output one line with a length $n$ binary string containing only $0,1$ that satisfies the condition. If there is no solution, output `-1`.

## Constraints | Test Point ID | Score | $n\leq$ | Special Property | | -----------: | -----------: | -----------: | -----------: | | $1\sim 2$ | $20$ | $5$ | None | | $3\sim 4$ | $20$ | $10^6$ | $n \bmod 4 = 0$ | | $5\sim 6$ | $20$ | $20$ | None | | $7 \sim 10$ | $40$ | $10^6$ | None | Translated by ChatGPT 5