#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(v) v.begin(), v.end()
typedef long long ll;

#include <bits/stdc++.h>
using namespace std;

#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b)) < EPS)

class Point{
  public:
  double x,y;
  
  Point(double x=0, double y=0): x(x),y(y) {}
  
  Point operator+(Point p){return Point(x+p.x,y+p.y);}
  Point operator-(Point &p){return Point(x-p.x,y-p.y);}
  Point operator*(double a){return Point(a*x,a*y);}
  Point operator/(double a){return Point(x/a,y/a);}
  
  double abs(){return sqrt(norm());}
  double norm(){return x*x+y*y;}
  
  bool operator<(const Point &p) const{
    return x != p.x ? x<p.x : y<p.y;
  }
  
  bool operator==(const Point &p) const{
    return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
  }
};
typedef Point Vector;

struct Segment{Point p1,p2;};
typedef Segment Line;

class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(), double r=0.0): c(c), r(r) {}
};

typedef vector<Point> Polygon;

double dot(Vector a,Vector b){
  return a.x*b.x+a.y*b.y;
}

double cross(Vector a,Vector b){
  return a.x*b.y-a.y*b.x;
}

bool isOrthgonal(Vector a,Vector b){
  return equals(dot(a,b), 0.0);
}

bool isParallel(Vector a,Vector b){
  return equals(cross(a,b), 0.0);
}

int main(){
  int q;
  cin>>q;
  
  Vector p0,p1,p2,p3;
  while(q--){
    cin>>p0.x>>p0.y>>p1.x>>p1.y>>p2.x>>p2.y>>p3.x>>p3.y;
    if(isOrthgonal(p1-p0,p3-p2)) cout<<1<<endl;
    else if(isParallel(p1-p0,p3-p2)) cout<<2<<endl;
    else cout<<0<<endl;
  }
      
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

For given two lines s1 and s2, print "2" if they are parallel, "1" if they are orthogonal, or "0" otherwise.

s1 crosses points p0 and p1, and s2 crosses points p2 and p3.

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xpi, ypi ≤ 10000
* p0 ≠ p1 and p2 ≠ p3.

Input

The entire input looks like:


q (the number of queries)
1st query
2nd query
...
qth query


Each query consists of integer coordinates of the points p0, p1, p2, p3 in the following format:


xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3


Output

For each query, print "2", "1" or "0".

Example

Input

3
0 0 3 0 0 2 3 2
0 0 3 0 1 1 1 4
0 0 3 0 1 1 2 2


Output

2
1
0

### Response

```cpp
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(v) v.begin(), v.end()
typedef long long ll;

#include <bits/stdc++.h>
using namespace std;

#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b)) < EPS)

class Point{
  public:
  double x,y;
  
  Point(double x=0, double y=0): x(x),y(y) {}
  
  Point operator+(Point p){return Point(x+p.x,y+p.y);}
  Point operator-(Point &p){return Point(x-p.x,y-p.y);}
  Point operator*(double a){return Point(a*x,a*y);}
  Point operator/(double a){return Point(x/a,y/a);}
  
  double abs(){return sqrt(norm());}
  double norm(){return x*x+y*y;}
  
  bool operator<(const Point &p) const{
    return x != p.x ? x<p.x : y<p.y;
  }
  
  bool operator==(const Point &p) const{
    return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
  }
};
typedef Point Vector;

struct Segment{Point p1,p2;};
typedef Segment Line;

class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(), double r=0.0): c(c), r(r) {}
};

typedef vector<Point> Polygon;

double dot(Vector a,Vector b){
  return a.x*b.x+a.y*b.y;
}

double cross(Vector a,Vector b){
  return a.x*b.y-a.y*b.x;
}

bool isOrthgonal(Vector a,Vector b){
  return equals(dot(a,b), 0.0);
}

bool isParallel(Vector a,Vector b){
  return equals(cross(a,b), 0.0);
}

int main(){
  int q;
  cin>>q;
  
  Vector p0,p1,p2,p3;
  while(q--){
    cin>>p0.x>>p0.y>>p1.x>>p1.y>>p2.x>>p2.y>>p3.x>>p3.y;
    if(isOrthgonal(p1-p0,p3-p2)) cout<<1<<endl;
    else if(isParallel(p1-p0,p3-p2)) cout<<2<<endl;
    else cout<<0<<endl;
  }
      
  return 0;
}

```