Sunake is in the form of a polygonal line consisting of n vertices (without self-intersection). First, Sunake-kun's i-th vertex is at (xi, yi). You can move continuously by translating or rotating, but you cannot deform (change the length of the polygonal line or the angle between the two line segments). y = 0 is the wall, and there is a small hole at (0, 0). Determine if you can move through this hole so that the whole thing meets y <0.

Constraints

* 2 ≤ n ≤ 1000
* 0 ≤ xi ≤ 109
* 1 ≤ yi ≤ 109
* Lines do not have self-intersections
* None of the three points are on the same straight line
* (xi, yi) ≠ (xi + 1, yi + 1)
* All inputs are integers

Input


n
x1 y1
.. ..
xn yn


Output

Output "Possible" if you can move through the hole, and "Impossible" if you can't.

Examples

Input

4
0 1
1 1
1 2
2 2


Output

Possible


Input

11
63 106
87 143
102 132
115 169
74 145
41 177
56 130
28 141
19 124
0 156
22 183


Output

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

typedef long long int ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pair<int, int> > vii;
#define rrep(i, m, n) for(int (i)=(m); (i)<(n);  (i)++)
#define erep(i, m, n) for(int (i)=(m); (i)<=(n); (i)++)
#define  rep(i, n)    for(int (i)=0; (i)<(n);  (i)++)
#define rrev(i, m, n) for(int (i)=(n)-1; (i)>=(m); (i)--)
#define erev(i, m, n) for(int (i)=(n); (i)>=(m); (i)--)
#define  rev(i, n)    for(int (i)=(n)-1; (i)>=0; (i)--)
#define vrep(i, c)    for(__typeof((c).begin())i=(c).begin(); i!=(c).end(); i++)
#define  ALL(v)       (v).begin(), (v).end()
#define pb            push_back
#define mp            make_pair
template<class T, class S> inline bool minup(T& m, const S x){ return m>(T)x ? (m=(T)x, true) : false; }
template<class T, class S> inline bool maxup(T& m, const S x){ return m<(T)x ? (m=(T)x, true) : false; }

static const int    INF = 1000000000;
static const ll     MOD = 1000000007LL;
static const double EPS = 1E-10;

template<typename T> T add(T x, T y){ if(abs(x+y) < EPS*(abs(x)+abs(y))) return 0; return x + y; }
template<typename T> inline bool semieq(T x, T y){ return abs(x - y) < EPS; }
template<typename T> inline bool semige(T x, T y){ return y - x < -EPS; }
template<typename T> inline bool semile(T x, T y){ return x - y < -EPS; }


struct Point : public complex<double>
{
public:
  Point(const double x = 0.0, const double y = 0.0) { this->real(x);  this->imag(y); }
  Point(const complex<double> w)  { this->real(w.real());  this->imag(w.imag()); }
  inline double dot(Point p){ return (conj(*this) * p).real(); }  // ??????
  inline double det(Point p){ return (conj(*this) * p).imag(); }  // ??????
};

namespace std
{
  inline bool operator < (const Point& a, const Point& b)
  {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}
typedef vector<Point> Polygon;
inline Point currPoint(vector<Point> P, int i){ return P[i]; }
inline Point nextPoint(vector<Point> P, int i){ return P[(i+1)%P.size()]; }
inline Point diffPoint(vector<Point> P, int i){ return nextPoint(P, i) - currPoint(P, i); }


int ccw(Point a, Point b, Point c)
{
  b -= a;
  c -= a;
  if(b.det(c) > 0.0)    return  1;         // counter clockwise
  if(b.det(c) < 0.0)    return -1;         // clockwise
  if(b.dot(c) < 0.0)    return  2;         // c--a--b on line
  if(norm(b) < norm(c)) return -2;         // a--b--c on line
  return 0;
}


struct Line : public vector<Point>
{
public:
  Line(){ }
  Line(const Point P, const Point Q){ this->pb(P);  this->pb(Q); }
  Line(double px, double py, double qx, double qy){ this->pb(Point(px, py));  this->pb(Point(qx, qy)); }
};
typedef Line Segment;



Polygon AndrewMonotoneChain(vector<Point> ps)
{
  int n = ps.size(), k = 0;
  sort(ps.begin(), ps.end());
  Polygon ch(2*n);
  for(int i=0; i<n; ch[k++]=ps[i++]) // lower-hull
    while(k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
  for(int i=n-2, t=k+1; i>= 0; ch[k++]=ps[i--]) // upper-hull
    while(k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
  ch.resize(k-1);
  return ch;
}

enum { OUT, ON, IN };
int convexContains(const Polygon& P, const Point& p)
{
  const int n = P.size();
  Point g = (P[0] + P[n/3] + P[2*n/3]) / 3.0; // inner-Point
  int a = 0, b = n;
  while (a+1 < b) { // invariant: c is in fan g-P[a]-P[b]
    int c = (a + b) / 2;
    if (semige(Point(P[a]-g).det(P[c]-g), 0.0)) { // angle < 180 deg
      if (semige(Point(P[a]-g).det(p-g), 0.0) && semile(Point(P[c]-g).det(p-g), 0.0)) b = c;
      else a = c;
    } else {
      if (semile(Point(P[a]-g).det(p-g), 0.0) && semige(Point(P[c]-g).det(p-g), 0.0)) a = c;
      else b = c;
    }
  }
  b %= n;
  if (semile(Point(P[a] - p).det(P[b] - p), 0.0)) return 0;
  if (semige(Point(P[a] - p).det(P[b] - p), 0.0)) return 2;
  return 1;
}


int n;
double x, y;
vector<Point> P;
Polygon G;

int main(int argc, char *argv[])
{
  cin >> n;
  rep(i, n){
    cin >> x >> y;
    P.pb(Point(x, y));
  }

  bool ok = true;
  rrep(i, 3, n){
    G.clear();
    copy(P.begin(), P.begin() + i, back_inserter(G));
    G = AndrewMonotoneChain(G);
    if(convexContains(G, P[i]) == IN){
      ok = false;
      break;
    }
  }
  
  if(ok) rrep(i, 0, n - 3){
    G.clear();
    copy(P.begin() + i + 1, P.end(), back_inserter(G));
    G = AndrewMonotoneChain(G);
    if(convexContains(G, P[i]) == IN){
      ok = false;
      break;
    }
  }

  puts(ok ? "Possible" : "Impossible");
  
  return 0;
}