Pairwise different distances#652

Pairwise different distances

4 seconds
64 megabytes
Medium

For a given natural number , construct a set of points on the Cartesian plane with integer coordinates such that all pairwise distances between points are distinct.

Input

The only line of the input file contains a natural number (N \leq 200) — the number of points in the set.

Output

Print the coordinates of the constructed set of points (each point should be on a separate line, and its coordinates separated by a space). The absolute value of each coordinate should not exceed . It is guaranteed that such a set exists. If there are multiple possible sets, you may output any of them.

Examples

Example 1

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