Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Long sequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA sequence *a*_{0}, *a*_{1}, ... is called a recurrent binary sequence, if each term *a*_{i} (*i* = 0, 1, ...) is equal to 0 or 1 and there exist coefficients such that

Note that such a sequence can be uniquely recovered from any *k*-tuple {*a*_{s}, *a*_{s + 1}, ..., *a*_{s + k - 1}} and so it is periodic. Moreover, if a *k*-tuple contains only zeros, then the sequence contains only zeros, so this case is not very interesting. Otherwise the minimal period of the sequence is not greater than 2^{k} - 1, as *k*-tuple determines next element, and there are 2^{k} - 1 non-zero *k*-tuples. Let us call a sequence long if its minimal period is exactly 2^{k} - 1. Your task is to find a long sequence for a given *k*, if there is any.

Input

Input contains a single integer *k* (2 ≤ *k* ≤ 50).

Output

If there is no long sequence for a given *k*, output "-1" (without quotes). Otherwise the first line of the output should contain *k* integer numbers: *c*_{1}, *c*_{2}, ..., *c*_{k} (coefficients). The second line should contain first *k* elements of the sequence: *a*_{0}, *a*_{1}, ..., *a*_{k - 1}. All of them (elements and coefficients) should be equal to 0 or 1, and at least one *c*_{i} has to be equal to 1.

If there are several solutions, output any.

Examples

Input

2

Output

1 1

1 0

Input

3

Output

0 1 1

1 1 1

Note

1. In the first sample: *c*_{1} = 1, *c*_{2} = 1, so *a*_{n} = *a*_{n - 1} + *a*_{n - 2} (*mod* 2). Thus the sequence will be:

so its period equals 3 = 2^{2} - 1.

2. In the second sample: *c*_{1} = 0, *c*_{2} = 1, *c*_{3} = 1, so *a*_{n} = *a*_{n - 2} + *a*_{n - 3} (*mod* 2). Thus our sequence is:

and its period equals 7 = 2^{3} - 1.

Periods are colored.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/24/2017 16:50:25 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|