public class point {
  float x,y;
  public point(float _x, float _y) {
    x = _x;
    y = _y;
  }  
  
  point minus(point p) {
    return new point(x-p.x,y-p.y);
  }
  float mag() {
    return sqrt(sq(x) + sq(y));  
  }
}

float dot(point a, point b, point c) {
  point AB = b.minus(a);  
  point BC = c.minus(b);
  return AB.x*BC.x + AB.y*BC.y;
}

float cross(point a, point b, point c) {
  point AB = b.minus(a);  
  point AC = c.minus(a);
  return AB.x*AC.y - AB.y*AC.x;  
}

float distance(point a, point b) {
  return (a.minus(b)).mag();
}

float linePointDistance(point a, point b, point c, boolean isSegment) {
  if (isSegment) {
    if (dot(a,b,c)>0) return distance(b,c);
    if (dot(b,a,c)>0) return distance(a,c);   
  }  
  return (cross(a,b,c)/distance(a,b));
}

point nearestPoint(point a, point b, point c, boolean isSegment) {
  if (isSegment) {
    if (dot(a,b,c)>0) return b;
    if (dot(b,a,c)>0) return a;   
  }  
  float segLength = distance(a,b);
  float segDist = (((c.x-a.x)*(b.x-a.x)) + ((c.y-a.y)*(b.y-a.y)))/(segLength*segLength);
  return new point(a.x+segDist*(b.x-a.x), a.y+segDist*(b.y-a.y));    
}