This is an answer-submission problem.

In the P 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 P universe such that when these organisms produce children in all possible pairs, the number of distinct children is maximized. 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

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

The output should contain exactly one line, consisting of $2\,000$ integers in the range $0 \sim 2^{20}-1$, 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

If your output is invalid, your score will be $0$.

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

Hack

The hack feature is not available for this problem.