Problem: Furik loves painting stars. A star is a shape that results if we take a regular pentagon and paint all diagonals in it. 

<image>

Recently he decided to teach Rubik to paint stars. After many years of training Rubik could paint stars easily. But now Furik decided to test Rubik and complicated the task. Rubik must paint n stars, observing the following rules:

  * all stars must be painted in a single move (i.e. it is forbidden to take the pen away from the paper); 
  * it is forbidden to paint the same segment of non-zero length more than once; 
  * the stars can intersect only in their vertexes; 
  * the length of a side of the regular pentagon, in which Rubik paints each star, must equal 10. 



Help Rubik to cope with this hard task.

Input

A single line contains an integer (1 ≤ n ≤ 100) — the number of stars to paint.

Output

On the first line print an integer m (1 ≤ m ≤ 5·n). On the next m lines print coordinates of m distinct points with accuracy of at least 9 and at most 100 digits after decimal point. All coordinates should not exceed 5000 in their absolute value. On each of the next n lines print 5 integers — the indexes of the points that form the given star in the clockwise or counterclockwise order. On the next line print 5·n + 1 integers — the numbers of points in the order, in which Rubik paints stars. That is, if number with index i is ai, and number with index i + 1 is ai + 1, then points with indexes ai and ai + 1 will have a segment painted between them. 

You can consider all m printed points indexed from 1 to m in the order, in which they occur in the output. Separate the numbers on the lines with whitespaces.

Note that the answer has an imprecise validation. Try to obtain as accurate a solution as possible. The validator performs all calculations considering that the absolute error of a participant's answer is not more than 10 - 8.

Examples

Input

1


Output

5
3.830127018922193 3.366025403784439
-3.601321235851749 10.057331467373021
0.466045194906253 19.192786043799030
10.411264148588986 18.147501411122495
12.490381056766580 8.366025403784439
1 2 3 4 5
1 3 5 2 4 1

Note

The initial position of points in the sample is:

<image>

The order in which Rubik can paint segments is:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double pi = acosl(-1);
const long double radian = 180 / pi;
const long double eps = 1e-12;
const int inf = 0x7f7f7f7f;
const long long infll = 0x7f7f7f7f7f7f7f7fll;
const long double infl = 1e20;
inline int sgn(const long double &x) { return (x > eps) - (x < -eps); }
inline int sgn(const long long &x) { return (x > 0) - (x < 0); }
inline long double sqr(const long double &x) { return x * x; }
inline long long sqr(const long long &x) { return x * x; }
inline long double refresh(const long double &x) {
  if (x < -1 + eps)
    return -1;
  else if (x > 1 - eps)
    return 1;
  else
    return x;
}
struct Point {
  long double x, y;
  Point() : x(0), y(0) {}
  Point(const long double &x, const long double &y) : x(x), y(y) {}
  long double angle() const { return atan2l(y, x); }
  long double angle(const Point &lhs, const Point &rhs) const {
    return (lhs - *this) ^ (rhs - *this);
  }
  long double length() const { return sqrtl(sqr(x) + sqr(y)); }
  long double length2() const { return sqr(x) + sqr(y); }
  long double distance(const Point &rhs) const {
    return (rhs - *this).length();
  }
  long double distance2(const Point &rhs) const {
    return (rhs - *this).length2();
  }
  Point rotate(const long double &a) const {
    long double c = cosl(a), s = sinl(a);
    return Point(x * c - y * s, x * s + y * c);
  }
  Point polar(const long double &r, const long double &t) const {
    return Point(x + r * cosl(t), y + r * sinl(t));
  }
  Point conjugate() const { return Point(x, -y); }
  Point unit(const long double &n = 1) const {
    long double l = length();
    return sgn(l) == 0 ? Point(n, 0) : Point(x / l * n, y / l * n);
  }
  Point normal(const bool &lft = true) const {
    return lft ? Point(-y, x) : Point(y, -x);
  }
  Point moderate() const { return *this * (this->quadrant() <= 4 ? -1 : 1); }
  long double vect(const Point &lhs, const Point &rhs) const {
    return (lhs - *this) * (rhs - *this);
  }
  long double scal(const Point &lhs, const Point &rhs) const {
    return (lhs - *this) & (rhs - *this);
  }
  Point project(const Point &p, const Point &q) const {
    return p + (q - p) * p.scal(q, *this) / p.distance2(q);
  }
  long double distance_to_line(const Point &p, const Point &q) const {
    return fabsl(p.vect(q, *this) / p.distance(q));
  }
  long double distance_to_segment(const Point &p, const Point &q) const {
    if (p.scal(q, *this) < 0)
      return p.distance(*this);
    else if (q.scal(p, *this) < 0)
      return q.distance(*this);
    else
      return this->distance_to_line(p, q);
  }
  bool on_line(const Point &p, const Point &q) const {
    return sgn(this->vect(p, q)) == 0;
  }
  bool on_halfline(const Point &p, const Point &q,
                   const bool &inclusive = true) const {
    if (*this == p)
      return inclusive;
    else
      return this->on_line(p, q) && sgn(p.scal(q, *this)) >= 0;
  }
  bool on_segment(const Point &p, const Point &q,
                  const bool &inclusive = true) const {
    if (*this == p || *this == q)
      return inclusive;
    else
      return this->on_line(p, q) && sgn(this->scal(p, q)) <= 0;
  }
  bool in_triangle(const Point &u, const Point &v, const Point &w,
                   const bool &inclusive = true) const {
    Point p[3] = {u, v, w};
    if (sgn(u.vect(v, w)) < 0) reverse(p, p + 3);
    for (int i = 0; i < 3; i++) {
      if (this->on_segment(p[i], p[(i + 1) % 3]))
        return inclusive;
      else if (sgn(this->vect(p[i], p[(i + 1) % 3])) < 0)
        return false;
    }
    return true;
  }
  bool in_angle(const Point &o, const Point &p, const Point &q,
                const bool &inclusive = true) const {
    if (this->on_halfline(o, p) || this->on_halfline(o, q)) return inclusive;
    int vp = sgn(o.vect(p, *this)), vq = sgn(o.vect(*this, q));
    if (sgn(o.vect(p, q)) >= 0)
      return vp > 0 && vq > 0;
    else
      return vp > 0 || vq > 0;
  }
  Point operator+(const Point &rhs) const {
    return Point(x + rhs.x, y + rhs.y);
  }
  Point operator-(const Point &rhs) const {
    return Point(x - rhs.x, y - rhs.y);
  }
  Point operator*(const long double &rhs) const {
    return Point(x * rhs, y * rhs);
  }
  Point operator/(const long double &rhs) const {
    return Point(x / rhs, y / rhs);
  }
  long double operator*(const Point &rhs) const {
    return x * rhs.y - y * rhs.x;
  }
  long double operator&(const Point &rhs) const {
    return x * rhs.x + y * rhs.y;
  }
  Point operator<<(const Point &rhs) const {
    return Point(x * rhs.x - y * rhs.y, x * rhs.y + y * rhs.x);
  }
  Point operator>>(const Point &rhs) const {
    return Point(x * rhs.x + y * rhs.y, -x * rhs.y + y * rhs.x) / rhs.length2();
  }
  long double operator^(const Point &rhs) const {
    int s = sgn(*this * rhs);
    long double a = acosl(
        refresh((long double)(*this & rhs) / this->length() / rhs.length()));
    return s < 0 ? -a : a;
  }
  bool operator==(const Point &rhs) const {
    return sgn(x - rhs.x) == 0 && sgn(y - rhs.y) == 0;
  }
  int quadrant() const {
    int xs = sgn(x), ys = sgn(y);
    if (xs == 0 && ys == 0)
      return 0;
    else if (xs < 0 && ys < 0)
      return 1;
    else if (xs == 0 && ys < 0)
      return 2;
    else if (xs > 0 && ys < 0)
      return 3;
    else if (xs > 0 && ys == 0)
      return 4;
    else if (xs > 0 && ys > 0)
      return 5;
    else if (xs == 0 && ys > 0)
      return 6;
    else if (xs < 0 && ys > 0)
      return 7;
    else
      return 8;
  }
  bool operator<(const Point &rhs) const {
    int lq = quadrant(), rq = rhs.quadrant();
    if (lq != rq)
      return lq < rq;
    else {
      int s = sgn(*this * rhs);
      return s != 0 ? s > 0 : sgn(length2() - rhs.length2()) < 0;
    }
  }
  bool on_left(const Point &rhs, const bool &inclusive = true) const {
    int s = sgn(*this * rhs), t = sgn(*this & rhs);
    return s == 0 ? t >= 0 || inclusive : s > 0;
  }
  bool on_right(const Point &rhs, const bool &inclusive = true) const {
    int s = sgn(*this * rhs), t = sgn(*this & rhs);
    return s == 0 ? t >= 0 || inclusive : s < 0;
  }
};
inline bool xycmp(const Point &lhs, const Point &rhs) {
  if (sgn(lhs.x - rhs.x) != 0)
    return lhs.x < rhs.x;
  else
    return lhs.y < rhs.y;
}
inline bool yxcmp(const Point &lhs, const Point &rhs) {
  if (sgn(lhs.y - rhs.y) != 0)
    return lhs.y < rhs.y;
  else
    return lhs.x < rhs.x;
}
const int side = 10;
const long double r = side / cosl(pi * 3 / 10) / 2;
const long double alpha[5] = {pi * 9 / 10, -pi * 3 / 10, pi / 2, -pi * 7 / 10,
                              pi / 10};
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  cout << n * 4 + 1 << endl;
  Point O, p;
  cout << fixed << setprecision(20);
  p = O.polar(r, alpha[0]);
  cout << p.x << ' ' << p.y << endl;
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < 5; j++) {
      p = O.polar(r, alpha[j]);
      cout << p.x << ' ' << p.y << endl;
    }
    O.x += r * cosl(pi / 10) * 2;
  }
  for (int i = 0; i < n; i++)
    cout << i * 4 + 1 << ' ' << i * 4 + 3 << ' ' << i * 4 + 5 << ' '
         << i * 4 + 2 << ' ' << i * 4 + 4 << endl;
  cout << 1;
  for (int i = 1; i <= n; i++) cout << ' ' << i * 4 + 1;
  for (int i = n - 1; i >= 0; i--) {
    for (int j = 3; j >= 0; j--) cout << ' ' << i * 4 + j + 1;
  }
  cout << endl;
  return 0;
}