Irrational pairwise distances#639

Irrational pairwise distances

0.5 seconds

64 megabytes

Easy

Construct a set of $N$ points on the Cartesian plane such that the following conditions are satisfied:

The coordinates of each point are integers;
The distance between any two distinct points is an irrational number;
No three points are collinear.

Input

The only line contains a natural number $N$ $(1 \leq N \leq 1000)$ (1 \leq N \leq 1000) — the number of points in the set.

Output

Output $N$ lines, each containing two integers — the coordinates of a point (separated by a space). The absolute value of each coordinate must not exceed $1000000$ .

It is guaranteed that such a set exists. If there are multiple possible sets, output any one of them.

Examples

Example 1

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(1 \leq N \leq 1000)