Problem: Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.

Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.

Input

The input consists of three lines, each containing a pair of integer coordinates xi and yi ( - 1000 ≤ xi, yi ≤ 1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.

Output

First print integer k — the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices.

Then print k lines, each containing a pair of integer — possible coordinates of the fourth point.

Example

Input

0 0
1 0
0 1


Output

3
1 -1
-1 1
1 1

Note

If you need clarification of what parallelogram is, please check Wikipedia page:

https://en.wikipedia.org/wiki/Parallelogram

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long OO = (long long)1e18;
const long long mod = (1e9) + 7;
const double PI = acos(-1.0);
int dx[]{-1, -1, -1, 0, 0, 1, 1, 1};
int dy[]{-1, 0, 1, -1, 1, -1, 0, 1};
double dis(pair<double, double> a, pair<double, double> b) {
  return sqrt(pow(a.first - b.first, 2) + pow(a.second - b.second, 2));
}
long long pd(long long x) {
  if (x == 0) return 1;
  if (x == 1) return 1;
  unsigned long long ans = 1;
  for (int i = 2; i <= x; i++) ans *= i;
  return ans;
}
void file() {}
const double eps = 1e-9;
struct point {
  double x, y;
  point() : x(0), y(0) {}
  point(const point& p) : x(p.x), y(p.y) {}
  point(const std::pair<double, double>& p) : x(p.first), y(p.second) {}
  point(const long double& a, const long double& b) : x(a), y(b) {}
  bool operator<(const point& p) const {
    return (fabs((x) - (p.x)) <= eps) ? ((y) < (p.y) - eps)
                                      : ((x) < (p.x) - eps);
  }
  bool operator>(const point& p) const {
    return (fabs((x) - (p.x)) <= eps) ? ((p.y) < (y)-eps) : ((p.x) < (x)-eps);
  }
  bool operator==(const point& p) const {
    return (fabs((x) - (p.x)) <= eps) && (fabs((y) - (p.y)) <= eps);
  }
  bool operator!=(const point& p) const { return !(*this == p); }
  bool operator<=(const point& p) const { return !(*this > p); }
  bool operator>=(const point& p) const { return !(*this < p); }
  point operator+(const point& p) const { return point(x + p.x, y + p.y); }
  point operator-(const point& p) const { return point(x - p.x, y - p.y); }
  point operator+(const double& v) const { return point(x + v, y + v); }
  point operator-(const double& v) const { return point(x - v, y - v); }
  point operator*(const double& v) const { return point(x * v, y * v); }
  point operator/(const double& v) const { return point(x / v, y / v); }
  point& operator+=(const point& p) {
    x += p.x;
    y += p.y;
    return *this;
  }
  point& operator-=(const point& p) {
    x -= p.x;
    y -= p.y;
    return *this;
  }
  point& operator+=(const double& v) {
    x += v;
    y += v;
    return *this;
  }
  point& operator-=(const double& v) {
    x -= v;
    y -= v;
    return *this;
  }
  point& operator*=(const double& v) {
    x *= v;
    y *= v;
    return *this;
  }
  point& operator/=(const double& v) {
    x /= v;
    y /= v;
    return *this;
  }
  friend point operator+(const double& v, const point& p) { return p + v; }
  friend point operator*(const double& v, const point& p) { return p * v; }
  double norm() const { return x * x + y * y; }
  double abs() const { return sqrt(x * x + y * y); }
  double arg() const { return atan2(y, x); }
  double dot(const point& p) const { return x * p.x + y * p.y; }
  double cross(const point& p) const { return x * p.y - y * p.x; }
  double proj(const point& p) const { return dot(p) / p.abs(); }
  point rot90() const { return point(-y, x); }
  point normalize() const {
    return ((fabs((x) - (0)) <= eps) && (fabs((y) - (0)) <= eps))
               ? point(0, 0)
               : (point(x, y) / abs());
  }
  point rotateCW(const double& t) const {
    return point(x * cos(t) + y * sin(t), y * cos(t) - x * sin(t));
  }
  point rotateCCW(const double& t) const {
    return point(x * cos(t) - y * sin(t), x * sin(t) + y * cos(t));
  }
  point rotateCW(const point& p, const double& t) const {
    return (*this - p).rotateCW(t) + p;
  }
  point rotateCCW(const point& p, const double& t) const {
    return (*this - p).rotateCCW(t) + p;
  }
  point reflect(const point& p) const {
    return point(2 * p.x - x, 2 * p.y - y);
  }
  point reflect(const point& p, const point& q) const {
    if (p == q) return reflect(p);
    point r(*this - p), s = q - p;
    r = point(r.x * s.x + r.y * s.y, r.x * s.y - r.y * s.x) / s.norm();
    r = point(r.x * s.x - r.y * s.y, r.x * s.y + r.y * s.x) + p;
    return r;
  }
  friend double norm(const point& p) { return p.norm(); }
  friend long double abs(const point& p) { return p.abs(); }
  friend double arg(const point& p) { return p.arg(); }
  friend double dot(const point& p, const point& q) { return p.dot(q); }
  friend double cross(const point& p, const point& q) { return p.cross(q); }
  friend double proj(const point& p, const point& q) { return p.proj(q); }
  friend point rot90(const point& p) { return p.rot90(); }
  friend point normalize(const point& p) { return p.normalize(); }
  friend point rotateCW(const point& p, const double& t) {
    return p.rotateCW(t);
  }
  friend point rotateCCW(const point& p, const double& t) {
    return p.rotateCCW(t);
  }
  friend point rotateCW(const point& p, const point& q, const double& t) {
    return p.rotateCW(q, t);
  }
  friend point rotateCCW(const point& p, const point& q, const double& t) {
    return p.rotateCCW(q, t);
  }
  friend point reflect(const point& p, const point& q) { return p.reflect(q); }
  friend point reflect(const point& p, const point& a, const point& b) {
    return p.reflect(a, b);
  }
  friend std::ostream& operator<<(std::ostream& out, const point& p) {
    out << (fabs(p.x) < eps ? 0 : p.x) << " ";
    out << (fabs(p.y) < eps ? 0 : p.y) << "\n";
    return out;
  }
};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  file();
  vector<point> v(3);
  for (int i = 0; i < 3; i++) cin >> v[i].x >> v[i].y;
  sort(((v).begin()), ((v).end()));
  set<point> st;
  do {
    st.insert(v[0] + (v[1] - v[2]));
    st.insert(v[0] - (v[1] - v[2]));
  } while (next_permutation(((v).begin()), ((v).end())));
  cout << 3 << endl;
  for (auto i : st) cout << i;
}