给定一个正整数 n，请输出 n 位格雷码序列。 第 i 个格雷码（i 从 0 开始编号）定义为 g(i) = i xor (i >> 1), 其中 xor 表示按位异或，>> 表示右移。请依次输出 i = 0, 1, ..., 2^n - 1 对应的 g(i)，每个格雷码用恰好 n 个字符的二进制串表示，不足 n 位时在高位（左侧）补 0。

有 n 个人，编号为 1 到 n。已知其中存在 m 对朋友关系，每对关系由两个编号 u 和 v 给出，表示 u 与 v 是朋友。 朋友关系是相互的，并且具有传递性：如果 A 与 B 是朋友，B 与 C 是朋友，那么 A 与 C 也属于同一个朋友圈。也就是说，只要两个人能通过若干条朋友 ...

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