A sequence a₀, a₁, ... 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 contains a single integer k (2 ≤ k ≤ 50).

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: c₁, c₂, ..., c_k (coefficients). The second line should contain first k elements of the sequence: a₀, a₁, ..., 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.