This is an answer-submission problem.

In the Wang Haoqing universe, the DNA of an organism is represented by an integer between $0$ and $2^{20}-1$. DNA consists of exactly $20$ genes. For a DNA represented by an integer $x$, it contains the $i$-th gene ($1 \le i \le 20$) if and only if the $i$-th bit (from least significant to most significant) in the binary representation of $x$ is $1$.

Furthermore, it has been observed that any two distinct adult organisms can produce a child whose DNA contains the $i$-th gene if and only if the DNA of both parents contains that gene.

You wish to generate $2\,000$ adult organisms in the Wang Haoqing universe such that when any two of these organisms produce a child, the number of distinct children is as large as possible. Two children are considered distinct if and only if the integers representing their DNA are different.

Formal Problem Statement

Construct $2\,000$ integers $x_0, x_1, \dots, x_{1999}$ in the range $[0, 2^{20})$ such that the size of the set $V = \{x_i \operatorname{and} x_j \mid 0 \le i < j < 2000\}$ is as large as possible.

Output Format

This is an answer-submission problem. You only need to submit a file named 1.out describing your construction.

The output should consist of a single line containing exactly $2\,000$ integers between $0$ and $2^{20}-1$, representing your construction.

The provided files include a sample output file sample.out, which you can use as a reference for the correct output format.

Subtasks

Please note that the maximum score for this problem is 50 points.

If your outputted construction is invalid, your score will be $0$.

Otherwise, let $X$ denote the number of distinct children in your construction (i.e., the size of the set $V$ in the formal problem statement). Then your score will be: