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SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008

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H. Hankel Matrix

Time limit: 1.0 second
Memory limit: 64 MB
A Hankel matrix is a matrix of the following form:
Problem illustration
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

Input contains the size of the matrix n, 1 ≤ n ≤ 100.

Output

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.

Samples

inputoutput
1
1
2
1
6
37
3
1
3
10
7
630
Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.
To submit the solution for this problem go to the Problem set: 1625. Hankel Matrix