Magic Power Assignment

The enchanted queen’s gems have been stolen by the Dark God of Gunala and hidden in one of the n domes of the Magic Castle (numbered from 1 to n). Each dome i can be assigned an integer magic power a_i. A configuration is said to allow an easy search for the Dark God if the following two conditions hold:

\(\sum_{i=1}^{n} a_i = 0\) and \(\prod_{i=1}^{n} a_i = n\).

Your task is to assign magic powers to the n domes so that the above conditions hold. It is known that a solution exists for some values of n (for example, n = 4 and n = 8). For other values, output -1 to indicate that no assignment is possible.

Note: In all configurations every a_i must be a nonzero integer.

inputFormat

The input consists of a single integer n (1 ≤ n ≤ 10⁹).

outputFormat

If there exists an assignment of nonzero integers a₁, a₂, ..., a_n satisfying \(\sum_{i=1}^{n} a_i = 0\) and \(\prod_{i=1}^{n} a_i = n\), output the n numbers separated by spaces on one line. Otherwise, output -1.

sample

4

1 -1 2 -2