时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
Special Judge, 64bit IO Format: %lld
题目描述
Nami will get a sequence of
positive integers
soon and she wants to divide it into two subsequences.
At first, Nami has two empty sequences and
. She will consider each integer in
in order, and append it to either
or
. Nami calls sequences
she gets in the end a division of
. Note that
and
are different and subsequences can be empty, so there are
ways to divide
into
and
, which means there are
possible divisions of
.
For a division, supposing that there are integers in
and
integers in
, Nami will call it a great division if and only if the following conditions hold:
Nami defines the greatness of as the number of different great divisions of
. Now Nami gives you a magic number
, and your task is to find a sequence
with the greatness equal to
for her.
Note that the length of should not exceed
and the positive integers in
should not exceed
.
If there are several possible sequences, you can print any of them. If there is no sequence with the greatness equal to , print
.
输入描述:
A single line contains an integer(
) - the magic number from Nami.
输出描述:
If there is no sequence with the greatness equal to
in a single line.
Otherwise, in the first line, print the length
(
) of the sequence
.
In the second line, print
(
) - the sequence for Nami.