#include <bits/stdc++.h>
const double EPS = 1e-4;
enum POSITION {
  ONLINE_FRONT = -2,
  CLOCKWISE,
  ON_SEGMENT,
  COUNTER_CLOCKWISE,
  ONLINE_BACK
};
struct Point {
  double x, y;
  Point(const double d = 0.0) : x(d), y(d) {}
  Point(const double x, const double y) : x(x), y(y) {}
};
struct Segment {
  Point initial, terminal;
  Segment(const Point& initial = 0, const Point& terminal = 0)
      : initial(initial), terminal(terminal) {}
  Segment(const double x1, const double y1, const double x2, const double y2)
      : initial(x1, y1), terminal(x2, y2) {}
};
struct Line {
  Point initial, terminal;
  Line(const Point& initial, const Point& terminal)
      : initial(initial), terminal(terminal) {}
  Line(const double x1, const double y1, const double x2, const double y2)
      : initial(x1, y1), terminal(x2, y2) {}
  Line(const Segment& s) : initial(s.initial), terminal(s.terminal) {}
};
bool relative_equal(const double d1, const double d2) {
  return d1 == 0 ? std::abs(d2) < EPS : std::abs((d1 - d2) / d1) < EPS;
}
bool operator==(const Point& lhs, const Point& rhs) {
  return relative_equal(lhs.x, rhs.x) && relative_equal(lhs.y, rhs.y);
}
bool operator<(const Point& lhs, const Point& rhs) {
  return relative_equal(lhs.x, rhs.x) ? lhs.y < rhs.y : lhs.x < rhs.x;
}
bool operator>(const Point& lhs, const Point& rhs) {
  return relative_equal(lhs.x, rhs.x) ? lhs.y > rhs.y : lhs.x > rhs.x;
}
bool operator!=(const Point& lhs, const Point& rhs) { return !(lhs == rhs); }
bool operator<=(const Point& lhs, const Point& rhs) { return !(lhs > rhs); }
bool operator>=(const Point& lhs, const Point& rhs) { return !(lhs < rhs); }
const Point operator+(const Point& lhs, const Point& rhs) {
  return Point(lhs.x + rhs.x, lhs.y + rhs.y);
}
const Point operator-(const Point& lhs, const Point& rhs) {
  return Point(lhs.x - rhs.x, lhs.y - rhs.y);
}
const Point operator*(const Point& lhs, const Point& rhs) {
  return Point(lhs.x * rhs.x, lhs.y * rhs.y);
}
const Point operator/(const Point& lhs, const Point& rhs) {
  return Point(lhs.x / rhs.x, lhs.y / rhs.y);
}
const Point operator-(const Point& p) { return Point(-p.x, -p.y); }
double abs(const Point& p) { return std::hypot(p.x, p.y); }
double norm(const Point& p) { return p.x * p.x + p.y * p.y; }
double dot(const Point& a, const Point& b) { return a.x * b.x + a.y * b.y; }
double cross(const Point& a, const Point& b) { return a.x * b.y - a.y * b.x; }
bool parallel(const Line& l1, const Line& l2) {
  return relative_equal(
      0.0, cross(l2.terminal - l2.initial, l1.terminal - l1.initial));
}
bool orthogonal(const Line& l1, const Line& l2) {
  return relative_equal(
      0.0, dot(l2.terminal - l2.initial, l1.terminal - l1.initial));
}
POSITION ccw(const Point& a, const Point& b, const Point& p) {
  Point v1 = b - a;
  Point v2 = p - a;
  if (cross(v1, v2) >= EPS) return COUNTER_CLOCKWISE;
  if (cross(v1, v2) <= -EPS) return CLOCKWISE;
  if (dot(v1, v2) <= -EPS) return ONLINE_BACK;
  if (norm(v1) < norm(v2)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
bool intersect(const Point& p1, const Point& p2) { return p1 == p2; }
bool intersect(const Point& p, const Segment& s) {
  return abs(p - s.initial) + abs(p - s.terminal) -
             abs(s.initial - s.terminal) <=
         EPS;
}
bool intersect(const Segment& s, const Point& p) { return intersect(p, s); }
bool intersect(const Point& p, const Line& l) {
  return !parallel(Line(p, l.initial), Line(p, l.terminal));
}
bool intersect(const Line& l, const Point& p) { return intersect(p, l); }
bool intersect(const Segment& s1, const Segment& s2) {
  return ccw(s1.initial, s1.terminal, s2.initial) *
                 ccw(s1.initial, s1.terminal, s2.terminal) <=
             0 &&
         ccw(s2.initial, s2.terminal, s1.initial) *
                 ccw(s2.initial, s2.terminal, s1.terminal) <=
             0;
}
bool intersect(const Segment& s, const Line& l) {
  auto v1 = l.terminal - l.initial;
  auto v2 = s.initial - l.initial;
  auto v3 = s.terminal - l.initial;
  return cross(v1, v2) * cross(v1, v3) <= EPS;
}
bool intersect(const Line& l, const Segment& s) { return intersect(s, l); }
bool intersect(const Line& l1, const Line& l2) {
  return !parallel(l1, l2) || intersect(l1.initial, l2);
}
Point projection(const Point& p, const Line& l) {
  auto v = l.initial - l.terminal;
  return l.initial + dot(p - l.initial, v) / norm(v) * v;
}
Point projection(const Line& l, const Point& p) { return projection(p, l); }
Point reflection(const Point& p, const Line& l) {
  return p + 2 * (projection(p, l) - p);
}
Point reflection(const Line& l, const Point& p) { return reflection(p, l); }
double distance(const Point& p1, const Point& p2) {
  auto p = p1 - p2;
  return hypot(p.x, p.y);
}
double distance(const Point& p, const Segment& s) {
  auto r = projection(s, p);
  return intersect(r, s)
             ? distance(p, r)
             : std::min(distance(p, s.initial), distance(p, s.terminal));
}
double distance(const Segment& s, const Point& p) { return distance(p, s); }
double distance(const Point& p, const Line& l) {
  return distance(p, projection(p, l));
}
double distance(const Line& l, const Point& p) { return distance(p, l); }
double distance(const Segment& s1, const Segment& s2) {
  return intersect(s1, s2)
             ? 0.0
             : std::min({distance(s1, s2.initial), distance(s1, s2.terminal),
                         distance(s2, s1.initial), distance(s2, s1.terminal)});
}
double distance(const Segment& s, const Line& l) {
  return intersect(s, l)
             ? 0.0
             : std::min(distance(s.initial, l), distance(s.terminal, l));
}
double distance(const Line& l, const Segment& s) { return distance(s, l); }
double distance(const Line& l1, const Line& l2) {
  return intersect(l1, l2) ? 0.0 : distance(l1.initial, l2);
}
const Point crosspoint(const Line& l1, const Line& l2) {
  assert(intersect(l1, l2));
  if (parallel(l1, l2)) return l1.initial;
  double A = cross(l1.terminal - l1.initial, l2.terminal - l2.initial);
  double B = cross(l1.terminal - l1.initial, l1.terminal - l2.initial);
  return l2.initial + B / A * (l2.terminal - l2.initial);
}
const Point crosspoint(const Segment& s, const Line& l) {
  assert(intersect(s, l));
  if (parallel(s, l)) return s.initial;
  return crosspoint(Line(s), l);
}
const Point crosspoint(const Line& l, const Segment& s) {
  return crosspoint(s, l);
}
const Point crosspoint(const Segment& s1, const Segment& s2) {
  assert(intersect(s1, s2));
  if (parallel(s1, s2)) {
    if (intersect(s1.initial, s2)) return s1.initial;
    if (intersect(s1.terminal, s2)) return s1.terminal;
    if (intersect(s2.initial, s1)) return s2.initial;
    if (intersect(s2.terminal, s1)) return s2.terminal;
  }
  return crosspoint(Line(s1), Line(s2));
}
std::ostream& operator<<(std::ostream& os, const Point& p) {
  os << "";
  os << "" << p.x << " " << p.y << "";
  return os;
}
std::ostream& operator<<(std::ostream& os, const Segment& s) {
  os << "segment: ";
  os << s.initial << " - " << s.terminal;
  return os;
}
std::ostream& operator<<(std::ostream& os, const Line& l) {
  os << "line: ";
  os << l.initial << " - " << l.terminal;
  return os;
}
using namespace std;
const int N = 16;
const int M = N * N;
int n;
Point vertex[N];
Segment edge[N];
int m;
Segment devided_edge[M];
int solve() {
  vector<set<Point>> devided_point(n);
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j) {
      Line l(vertex[i], vertex[j]);
      for (int k = 0; k < n; ++k)
        if (intersect(edge[k], l))
          devided_point[k].insert(crosspoint(edge[k], l));
    }
  m = 0;
  for (int i = 0; i < n; ++i) {
    devided_point[i].insert(edge[i].initial);
    devided_point[i].insert(edge[i].terminal);
    auto cur = begin(devided_point[i]), pre = begin(devided_point[i]);
    for (++cur; cur != end(devided_point[i]); pre = cur++)
      devided_edge[m++] = {*pre, *cur};
  }
  set<tuple<int, int>> memo;
  int res = n;
  for (int bit = 1; bit < (1 << n) - 1; ++bit) {
    if (res <= __builtin_popcount(bit)) continue;
    bool ok = true;
    for (int i = 0; i < m; ++i) {
      bool covered = false;
      for (int v = 0; v < n; ++v)
        if ((bit >> v) & 1) {
          if (memo.count(tuple<int, int>(i, v))) {
            covered = true;
            break;
          }
          bool same_edge = false;
          for (int j = 0; j < n; ++j)
            if (intersect(edge[j], devided_edge[i]))
              if (vertex[v] == edge[j].initial || vertex[v] == edge[j].terminal)
                same_edge = true;
          if (same_edge) {
            covered = true;
            break;
          }
          bool blocked = false;
          bool outside = false;
          for (Segment s : {Segment(vertex[v], devided_edge[i].initial),
                            Segment(vertex[v], devided_edge[i].terminal)}) {
            if (blocked || outside) break;
            for (int j = 0; j < n; ++j)
              if (intersect(s, edge[j])) {
                auto cp = crosspoint(s, edge[j]);
                if (cp == s.initial || cp == s.terminal) continue;
                if (cp == edge[j].initial || cp == edge[j].terminal) continue;
                blocked = true;
                break;
              }
            if (blocked || outside) break;
            set<Point> touch = {s.initial, s.terminal};
            for (int j = 0; j < n; ++j)
              if (intersect(s, edge[j])) {
                if (parallel(s, edge[j])) {
                  touch.insert(edge[j].initial);
                  touch.insert(edge[j].terminal);
                } else {
                  touch.insert(crosspoint(s, edge[j]));
                }
              }
            auto cur = begin(touch), pre = begin(touch);
            for (++cur; cur != end(touch); pre = cur++) {
              auto p = (*pre + *cur) / 2.0;
              bool in = false;
              for (int j = 0; j < n; ++j) {
                if (intersect(p, edge[j])) {
                  in = true;
                  break;
                }
                auto a = edge[j].initial - p;
                auto b = edge[j].terminal - p;
                if (a.y > b.y) swap(a, b);
                if (a.y < EPS && EPS <= b.y && cross(a, b) < EPS) in = !in;
              }
              if (!in) outside = true;
              if (outside) break;
            }
          }
          if (blocked) continue;
          if (outside) continue;
          covered = true;
          memo.insert(tuple<int, int>(i, v));
        }
      if (!covered) ok = false;
      if (!ok) break;
    }
    if (ok) res = min(res, __builtin_popcount(bit));
  }
  return res;
}
int main() {
  while (cin >> n, n) {
    for (int i = 0; i < n; ++i) {
      double x, y;
      cin >> x >> y;
      vertex[i] = {x, y};
      if (0 < i) edge[i - 1] = {vertex[i - 1], vertex[i]};
    }
    edge[n - 1] = {vertex[n - 1], vertex[0]};
    cout << solve() << endl;
  }
}
