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Chips

Time limit 1 second
Memory limit 128 MiB

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 data

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

Output data

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

Input example #1
3
Output example #1
1 2 -1 3 1