Bob loves absolutely even arrays. For an array , let
be the number of subarrays with a non-negative sum, and
be the number of subarrays with a negative sum. An absolutely even array of size
is one which has the minimum absolute difference
over all possible arrays of size
. Please give Bob an example of an absolutely even array.
Constraints
Subtask 1 [30%]
Subtask 2 [70%]
No additional constraints.
Input Specification
The first and only line contains the integer .
Output Specification
The first and only line of your output should contain space-separated integers
, an array
which minimizes the value of
.
must hold.
Sample Input
3
Sample Output
1 -3 2
Explanation for Sample
and
are both equal to
. The
subarrays with a non-negative sum are
,
, and
. The
subarrays with a negative sum are
,
, and
. The value of
is
, which is minimal.
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