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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.

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