Chips

Given a strip of cells numbered from $1$ to $n$. It is allowed to remove or place a chip on the first cell or on the cell following the leftmost chip. The string is initially empty. It is required to occupy all the cells.

Input

One positive integer $n(1\le n\le 10)$.

Output

Print the sequence of cell numbers with which the action is performed. If a chip is removed, the cell number should be printed with a minus sign. The number of actions should not exceed $10^4$. If there are multiple solutions, print any of them.

Examples