Problem: Petya has recently started working as a programmer in the IT city company that develops computer games.

Besides game mechanics implementation to create a game it is necessary to create tool programs that can be used by game designers to create game levels. Petya's first assignment is to create a tool that allows to paint different arrows on the screen.

A user of this tool will choose a point on the screen, specify a vector (the arrow direction) and vary several parameters to get the required graphical effect. In the first version of the program Petya decided to limit parameters of the arrow by the following: a point with coordinates (px, py), a nonzero vector with coordinates (vx, vy), positive scalars a, b, c, d, a > c.

The produced arrow should have the following properties. The arrow consists of a triangle and a rectangle. The triangle is isosceles with base of length a and altitude of length b perpendicular to the base. The rectangle sides lengths are c and d. Point (px, py) is situated in the middle of the triangle base and in the middle of side of rectangle that has length c. Area of intersection of the triangle and the rectangle is zero. The direction from (px, py) point to the triangle vertex opposite to base containing the point coincides with direction of (vx, vy) vector.

Enumerate the arrow points coordinates in counter-clockwise order starting from the tip.

<image>

Input

The only line of the input contains eight integers px, py, vx, vy ( - 1000 ≤ px, py, vx, vy ≤ 1000, vx2 + vy2 > 0), a, b, c, d (1 ≤ a, b, c, d ≤ 1000, a > c).

Output

Output coordinates of the arrow points in counter-clockwise order. Each line should contain two coordinates, first x, then y. Relative or absolute error should not be greater than 10 - 9.

Examples

Input

8 8 0 2 8 3 4 5


Output

8.000000000000 11.000000000000
4.000000000000 8.000000000000
6.000000000000 8.000000000000
6.000000000000 3.000000000000
10.000000000000 3.000000000000
10.000000000000 8.000000000000
12.000000000000 8.000000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline void normal(long long int& a) { a = (a + 1000000007) % 1000000007; }
inline int modMul(long long int a, long long int b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a * b) % 1000000007;
}
inline int modAdd(long long int a, long long int b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a + b) % 1000000007;
}
inline int modSub(long long int a, long long int b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline int modPow(long long int b, long long int p) {
  int r = 1;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1;
  }
  return r;
}
inline int modInv(int a) { return modPow(a, 1000000007 - 2); }
inline int modDiv(int a, int b) { return modMul(a, modInv(b)); }
inline int fact(int r) {
  int ans = 1;
  while (r) ans = modMul(ans, r), r--;
  return ans;
}
inline int invfact(int r) {
  int ans = 1;
  while (r) ans = modMul(ans, modInv(r)), r--;
  return ans;
}
inline double dgcd(double a, double b) {
  if (a < b) return dgcd(b, a);
  if (b < .0001) return a;
  return dgcd(b, fmod(a, b));
}
const long long int N = 2e5 + 2;
const long long int INF = 1e17;
clock_t start;
mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
template <typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& q) {
  in >> q.first >> q.second;
  return in;
}
template <typename T1, typename T2>
ostream& operator<<(ostream& out, pair<T1, T2>& q) {
  out << q.first << " " << q.second;
  return out;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(pair<T1, T2> p1, pair<T1, T2> p2) {
  return {p1.first + p2.first, p1.second + p2.second};
}
template <typename T1, typename T2>
pair<T1, T2> operator-(pair<T1, T2> p1, pair<T1, T2> p2) {
  return {p1.first - p2.first, p1.second - p2.second};
}
long long int power(long long int base, long long int exp) {
  long long int res = 1;
  while (exp > 0) {
    if (exp % 2 == 1) res = (res * base) % 1000000007;
    base = (base * base) % 1000000007;
    exp /= 2;
  }
  return res % 1000000007;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
int main() {
  cout << fixed << setprecision(18);
  ;
  long long int z1, z2, z3, z4, z5, z6, z7, z8;
  cin >> z1 >> z2 >> z3 >> z4 >> z5 >> z6 >> z7 >> z8;
  double a = z1, b = z2, c = z3, d = z4, e = z5, f = z6, g = z7, h = z8;
  double z = sqrt(c * c + d * d);
  double x, y;
  x = a + f * (c / z);
  y = b + f * (d / z);
  cout << x << " " << y << '\n';
  x = a + (-e / 2) * (d / z);
  y = b + (-e / 2) * (-c / z);
  cout << x << " " << y << '\n';
  x = a + (-g / 2) * (d / z);
  y = b + (-g / 2) * (-c / z);
  cout << x << " " << y << '\n';
  x = a + h * (-c / z) + (-g / 2) * (d / z);
  y = b + h * (-d / z) + (-g / 2) * (-c / z);
  cout << x << " " << y << '\n';
  x = a + h * (-c / z) + (g / 2) * (d / z);
  y = b + h * (-d / z) + (g / 2) * (-c / z);
  cout << x << " " << y << '\n';
  x = a + (g / 2) * (d / z);
  y = b + (g / 2) * (-c / z);
  cout << x << " " << y << '\n';
  x = a + (e / 2) * (d / z);
  y = b + (e / 2) * (-c / z);
  cout << x << " " << y << '\n';
  return 0;
}