19083번 - Numb 스페셜 저지다국어

문제

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,ドル 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 $n$.

입력

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

출력

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.

제한

힌트