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3 초 (추가 시간 없음) 512 MB 6 4 3 60.000%

문제

We say a set of points are concyclic if they all lie on the circumference of a circle. The task is: given an integer n, find a circle centered at (0, 0) such that there are at least n distinct concyclic integral points lying on it.

Note: Integral points are points with integral coordinates.

입력

The input is a line containing a positive integer n.

출력

Output n + 1 lines. The first line contains an integer r indicating the radius of the circle. Each of the following lines contains two integers x and y such that point (x, y) lies on the circle.

제한

  • 1 ≤ n ≤ 1000
  • This problem uses a special checker so you don’t have to output the minimum radius r.
  • Each token in your output cannot exceed 30 characters.
  • Every point in your output must be unique.
  • The size of your code must be no greater than 256 kilobytes.

예제 입력 1

1

예제 출력 1

100
100 0

예제 입력 2

7

예제 출력 2

5
5 0
0 5
-5 0
3 4
3 -4
-3 -4
-3 4