Convex Hull Generator

You have to generate a convex polygon which

• has N points
• each Xi is distinct and is between 1 and N
• Each Yi is positive and less than 1010

There can be many many convex polygons that fits this description. You have to print any one of them.

Input

The only line in input is N (3 ≤ N ≤ 100000).

Output

Print N lines. Each line will contain two integers Xi and Yi.

Sample

3

1 1
2 4
3 8