#include <bits/stdc++.h>
#define REP(i,n) for(int i=0; i<(int)(n); ++i)

using namespace std;

typedef complex<double> Point;
const double EPS = 1e-8;

int sign(double a){
    if(a > EPS) return +1;
    if(a < -EPS) return -1;
    return 0;
}
double dot(Point a, Point b){
    return real(conj(a) * b);
}
double cross(Point a, Point b){
    return imag(conj(a) * b);
}
int ccw(Point a, Point b, Point c) {
    b -= a; c -= a;
    double len = abs(b) * abs(c); // テゥツ?淌」ツ?陛」ツ?古ヲツーツ療」ツ?ォテ」ツ?ェテ」ツつ凝」ツ?ィテ」ツ?催」ツ?ッ1テ」ツ?ォテ」ツ?凖」ツつ?
    if (cross(b, c) > +len * EPS)   return +1; // テ・ツ渉催ヲツ卍づィツィツ暗・ツ崢榲」ツつ?
    if (cross(b, c) < -len * EPS)   return -1; // テヲツ卍づィツィツ暗・ツ崢榲」ツつ?
    if (dot(b, c) < 0)     return +2; // c--a--b テ」ツ?ョテゥツ??ァツ閉ェテ」ツ?ァテ、ツクツ?ァツ崢エテァツキツ堙、ツクツ?
    if (norm(b) < norm(c)) return -2; // a--b--c テ」ツ?ョテゥツ??ァツ閉ェテ」ツ?ァテ、ツクツ?ァツ崢エテァツキツ堙、ツクツ?
    return 0;                         // テァツつケテ」ツ?古ァツキツ堙・ツ按?bテ、ツクツ甘」ツ?ォテ」ツ?づ」ツつ?
}
struct Line : public vector<Point> {
    Line() {}
    Line(const Point& a, const Point& b) {
        push_back(a); push_back(b);
    }
    Point vector() const {
        return back() - front();
    }
};
typedef vector<Point> Polygon; // テ・ツ渉催ヲツ卍づィツィツ暗・ツ崢榲」ツつ甘」ツつ津、ツサツョテ・ツョツ?
Point crosspointLL(Line l, Line m){
    double A = cross(l.vector(), m.vector());
    double B = cross(l.vector(), l[1] - m[0]);
    if(sign(A) == 0 && sign(B) == 0) return m[0]; // テ、ツコツ古ァツ崢エテァツキツ堙」ツ?古ゥツ?催」ツ?ェテ」ツ?」テ」ツ?ヲテ」ツ??」ツつ?
    if(sign(A) == 0) assert(false); // テァツ崢エテァツキツ堙」ツ?古、ツコツ、テ」ツつ湘」ツつ嘉」ツ?ェテ」ツ??
    return m[0] + m.vector() * B / A;
}
// テ、ツクツ。テァツォツッテ」ツつ津・ツ青ォテ」ツ?セテ」ツ?ェテ」ツ??
bool intersectSP(Line s, Point p) {
    return ccw(s[0], s[1], p) == 0 && abs(s[0] - p) > EPS && abs(s[1] - p) > EPS;
}
bool equalLL(Line l, Line m){
    return sign(cross(l.vector(), m[0] - l[0])) == 0;
}
bool intersectLS(Line l, Line s) {
    // テァツ崢エテァツキツ嗟テ」ツ?ォテ」ツ?、テ」ツ??」ツ?ヲテ」ツ??ァツキツ堙・ツ按?テ」ツ?ョテァツォツッテァツつケテ」ツ?古ァツ閉ーテ」ツ?ェテ」ツつ凝・ツ?エテ」ツ?ォテ」ツ?づ」ツつ?
    return sign(cross(l.vector(), s[0] - l[0]) * cross(l.vector(), s[1] - l[0])) <= 0;
}
bool intersectSS(Line s, Line t) {
    bool f = ccw(s[0], s[1], t[0]) * ccw(s[0], s[1], t[1]) <= 0 && ccw(t[0], t[1], s[0]) * ccw(t[0], t[1], s[1]) <= 0;
    if(!f) return false;
    Point cp = crosspointLL(s, t);
    return intersectSP(s, cp) && intersectSP(t, cp);
}

Point curr(const Polygon& P, int x){
    return P[x];
}
Point next(const Polygon& P, int x){
    return P[(x + 1) % P.size()];
}

enum { OUT, ON, IN };
int contains(const Polygon& P, const Point& p){
    // テァツつケpテ」ツ?凝」ツつ嘉・ツ債甘ァツ崢エテァツキツ堙」ツつ津」ツ?イテ」ツ?催」ツ??ィツセツコテ」ツ?ィテ、ツコツ、テ・ツキツョテ」ツ?凖」ツつ凝・ツ崢榲ヲツ閉ーテ」ツつ津ヲツ閉ーテ」ツ?暗」ツつ?
    bool in = false;
    for(int i = 0; i < P.size(); i++){
        Point a = curr(P, i) - p;
        Point b = next(P, i) - p;
        if(a.imag() > b.imag()) swap(a, b);
        // aテ」ツ?凝」ツつ叡テ」ツ?ョテァツ崢エテァツキツ堙」ツ?軽=0テ」ツ?ィテ、ツコツ、テ」ツつ湘」ツつ甘」ツ??」ツ?敕」ツ?ョテ、ツコツ、テァツつケテ」ツ?ッテ・ツ篠淌ァツつケテ」ツ?ョテ・ツ渉ウテ・ツ?エテ」ツ?ァテ」ツ?づ」ツつ?
        if(a.imag() <= 0 && 0 < b.imag() && cross(a, b) < 0){ 
            in = !in;
        }
        if(sign(cross(a, b)) == 0 && sign(dot(a, b)) <= 0) return ON;
    }
    return in ? IN : OUT;
}

bool arrivable(Point bp, Point tp, const vector<Line>& poly_line, const Polygon& P){
    if(contains(P, 0.5 * (bp + tp)) == OUT) return false;

    Line cat(bp, tp);
    for(int k = 0; k < poly_line.size(); k++){
        Line pol = poly_line[k];
        if(equalLL(cat, pol)) continue;
        if(intersectSS(cat, pol)) return false;
    }

    return true;
}

int main(){
    int N;
    while(cin >> N && N){
        Polygon P(N);
        for(int i = 0; i < N; i++){
            double x, y;
            cin >> x >> y;
            P[i] = Point(x, y);
        }

        vector<Line> poly_line(N);
        for(int i = 0; i < N; i++){
            poly_line[i] = Line(P[i], P[(i + 1) % P.size()]);
            //fprintf(stderr, "line(%f, %f, %f, %f);\n",
                    //P[i].real() * 100, P[i].imag() * 100, P[(i + 1) % P.size()].real() * 100, P[(i + 1) % P.size()].imag() * 100);
        }

        vector<Point> cand_point = P; // テ・ツ?凖ィツ」ツ愿ァツつケ
        for(int i = 0; i < N; i++)
        for(int j = 0; j < N; j++){
            if(i == j) continue;
            Point bp = P[i], ep = P[j];
            Line cat(bp, ep);

            bool is_cross = false;
            Point cross_p;
            Line cross_l;
            int cross_idx;
            for(int k = 0; k < N; k++){
                Line pol = poly_line[k];

                if(equalLL(cat, pol)) continue;
                if(!intersectLS(cat, pol)) continue;

                Point cp = crosspointLL(cat, pol);

                if(!intersectSP(pol, cp)) continue;

                assert(abs(ccw(cat[0], cat[1], cp)) != 1);
                if(dot(cat.vector(), cp - cat[0]) < 0) continue; // true??
                //if(ccw(cat[0], cat[1], cp) != -2) continue; // true???

                if(!is_cross){
                    is_cross = true;
                    cross_p = cp; cross_l = pol;
                    cross_idx = k;
                }else if(abs(cross_p - cat[0]) > abs(cp - cat[0])){
                    cross_p = cp; cross_l = pol;
                    cross_idx = k;
                }

            }
            if(is_cross){
                //fprintf(stderr, "o : line(p[%d] = (%.0f, %.0f), p[%d] = (%.0f, %.0f)) has intersect\n", i, bp.real(), bp.imag(), j, ep.real(), ep.imag());
                //fprintf(stderr, "    line[%d]((%.0f, %.0f), (%.0f, %.0f)) , cross (%f. %f) \n",
                        //cross_idx, cross_l[0].real(), cross_l[0].imag(), cross_l[1].real(), cross_l[1].imag(), cross_p.real(), cross_p.imag());
                //fprintf(stderr, "circle(%f, %f, 5.0);\n", cross_p.real() * 100, cross_p.imag() * 100);
                cand_point.push_back(cross_p + cross_l.vector() * EPS);
                cand_point.push_back(cross_p - cross_l.vector() * EPS);
            }else{
                //fprintf(stderr, "x : line(p[%d] = (%.0f, %.0f), p[%d] = (%.0f, %.0f)) has no intersect\n", i, bp.real(), bp.imag(), j, ep.real(), ep.imag());
            }
        }

        vector<vector<bool>> is_arrivable(N, vector<bool>(cand_point.size(), false));
        for(int i = 0; i < N; i++)
        for(int j = 0; j < cand_point.size(); j++){
            Point bp = P[i], tp = cand_point[j];
            is_arrivable[i][j] = arrivable(bp, tp, poly_line, P);
            //fprintf(stderr, "%c : p[%d] -> (%f, %f)\n", is_arrivable[i][j] ? 'o' : 'x', i, cand_point[j].real(), cand_point[j].imag());
            if(i == 0 && !is_arrivable[i][j]){
                //fprintf(stderr, "line(%f, %f, %f, %f)\n", bp.real() * 100, bp.imag() * 100, tp.real() * 100, tp.imag() * 100);
            }
        }

        int ans = N;
        for(int s = 1; s < (1 << N); s++){
            int bits = __builtin_popcount(s);
            if(bits >= ans) continue;
            vector<bool> ok(cand_point.size(), false);
            for(int i = 0; i < N; i++) if(s >> i & 1)
                for(int j = 0; j < cand_point.size(); j++)
                    ok[j] = ok[j] || is_arrivable[i][j];

            bool is_answer = true;
            for(int i = 0; i < cand_point.size(); i++) if(!ok[i]){
                is_answer = false;
                break;
            }

            if(is_answer) {
                ans = bits;
            }
        }

        cout << ans << endl;
    }
    return 0;
}