给定一个偶数 $n$。请构造一个由 $n$ 个二进制位组成的二进制数 $a = \overline{a_1 a_2 \dots a_n}$，使得该数能被 $n$ 整除，且对于 $i = 1, 2, \dots, n$，所有数 $\overline{a_1 a_2 \dots a_i}$（即 $a$ 的二进制前缀）模 $n$ 的余数各不相同。
输入仅一行，包含一个整数 $n$ ($2 \le n \le 1000$，$n$ 为偶数)。
输出所求的 $n$ 位二进制数 $\overline{a_1 a_2 \dots a_n}$。不允许有前导零。如果存在多个可能的答案，输出其中任意一个即可。题目保证在这些约束条件下至少存在一个解。
2
10
4
1100
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