A15967 | XOR Partition

For a set of integers $S$ , let's define its cost as the minimum value of $x \oplus y$ among all pairs of different integers from the set (here, $\oplus$ denotes bitwise XOR). If there are less than two elements in the set, its cost is equal to $2^{30}$ .

You are given a set of integers $\{a_1, a_2, \dots, a_n\}$ . You have to partition it into two sets $S_1$ and $S_2$ in such a way that every element of the given set belongs to exactly one of these two sets. The value of the partition is the minimum among the costs of $S_1$ and $S_2$ .

Find the partition with the maximum possible value.

The first line contains $n$ ( $2 \le n \le 200000$ ) — the number of elements in the set.

The second line contains $n$ distinct integers $a_1$ , $a_2$ , ..., $a_n$ ( $0 \le a_i < 2^{30}$ ) — the elements of the set.

Print a string $n$ characters 0 and/or 1 describing the partition as follows: the $i$ -th character should be 0 if the element $a_i$ belongs to $S_1$ , otherwise, that character should be 1.

If there are multiple optimal answers, print any of them.