19083번 - Numb 스페셜 저지다국어

You are given an even integer $n$. Construct a binary number $a = \overline{a_1 a_2 \ldots a_n}$ consisting of $n$ binary digits such that it is divisible by $n$, and all numbers $\overline{a_1 a_2 \ldots a_i}$ (the prefixes of $a$ in binary notation) for $i = 1, 2, \ldots, n$ have different remainders modulo $n$.

The only line of input contains an integer $n$ ($2 \le n \le 1000$, $n$ is even).

Print the desired number $\overline{a_1 a_2 \ldots a_n}$ as a string of $n$ binary digits. Leading zeroes are disallowed. If there are several possible answers, print any one of them. It is guaranteed that at least one answer exists under these constraints.