Problem: Polycarpus loves convex polygons, especially if all their angles are the same and all their sides are different. Draw for him any such polygon with the given number of vertexes.

Input

The input contains a single integer n (3 ≤ n ≤ 100) — the number of the polygon vertexes.

Output

Print n lines, containing the coordinates of the vertexes of the n-gon "xi yi" in the counter clockwise order. The coordinates of the vertexes shouldn't exceed 106 in their absolute value. The side lengths should fit within limits [1, 1000] (not necessarily integer). Mutual comparing sides and angles of your polygon during the test will go with precision of 10 - 3.

If there is no solution, print "No solution" (without the quotes).

Examples

Input

8


Output

1.000 0.000
7.000 0.000
9.000 2.000
9.000 3.000
5.000 7.000
3.000 7.000
0.000 4.000
0.000 1.000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double pi = acos(-1.0);
const long double _eps = 0.001;
const int N = 103;
inline double rnd() { return rand() * 1.0 / RAND_MAX; }
int main() {
  srand(time(0));
  int n;
  long double x[N], y[N];
  x[0] = y[0] = 0;
  cin >> n;
  if (n < 5) return puts("No solution"), 0;
  long double ang = 0;
  long double delta = 2 * pi / n;
  for (;;) {
    long double d = rnd() * 512;
    double eps = _eps + (rand() % 10 * 0.0001);
    for (int i = 1; i < n - 1; i++) {
      ang += delta;
      x[i] = x[i - 1] + (d + eps * (i)) * cos(ang);
      y[i] = y[i - 1] + (d + eps * (i)) * sin(ang);
    }
    ang += delta;
    long double x1 = x[0], y1 = y[0], x2 = x[n - 2], y2 = y[n - 2];
    long double a1 = -cos(ang + delta), b1 = -sin(ang + delta);
    long double a2 = cos(ang), b2 = sin(ang);
    a2 *= -1, b2 *= -1;
    x2 -= x1, y2 -= y1;
    long double s = (x2 * b2 - y2 * a2) / (a1 * b2 - b1 * a2);
    x[n - 1] = x1 + s * a1;
    y[n - 1] = y1 + s * b1;
    auto sqr = [](long double x) { return x * x; };
    auto dis = [x, y, sqr](int i, int j) {
      return sqrt(sqr(x[i] - x[j]) + sqr(y[i] - y[j]));
    };
    vector<long double> tmp;
    tmp.clear();
    for (int i = 0; i < n; i++) tmp.push_back(dis(i, (i + 1) % n));
    sort(tmp.begin(), tmp.end());
    int flag = 1;
    for (int i = 0; i < n - 1; i++)
      if (tmp[i] + 0.001 >= tmp[i + 1]) {
        flag = 0;
        break;
      }
    if (flag) break;
  }
  for (int i = 0; i < n; i++)
    printf("%.10lf %.10lf\n", (double)x[i], (double)y[i]);
  ;
  return 0;
}