A Hankel matrix is a matrix of the following form:
Find an integer Hankel matrix of the given size with all non-negative elements and with determinant equal to one. Moreover, all its square submatrices containing upper left cell must also have determinant equal to one.
Input contains the size of the matrix n, 1 ≤ n ≤ 100.
Output non-negative integers α1, α2, …, α2n−1 from which the matrix is built, one per line. All αi shouldn't have more than 300 decimal digits. You may assume that such numbers always exist.
Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.