A Hankel matrix is a matrix of the following form:
Find an integer Hankel matrix of the given size with all nonnegative 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 nonnegative integers α_{1}, α_{2}, …, α_{2n−1} from which the matrix is built, one per line. All α_{i} shouldn't have more than 300 decimal digits. You may assume that such numbers always exist.
Samples
input  output 

1
 1

2
 1
6
37

3
 1
3
10
7
630

Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.